5543:
terms. Typical multiparameter equations of state use upwards of 50 fluid specific parameters, but are able to represent the fluid's properties with high accuracy. Multiparameter equations of state are available currently for about 50 of the most common industrial fluids including refrigerants. The IAPWS95 reference equation of state for water is also a multiparameter equations of state. Mixture models for multiparameter equations of state exist, as well. Yet, multiparameter equations of state applied to mixtures are known to exhibit artifacts at times.
6038:
10726:
89:
1659:
5551:
4606:
10233:
5217:. Hence, physically based equations of state model the effect of molecular size, attraction and shape as well as hydrogen bonding and polar interactions of fluids. In general, physically based equations of state give more accurate results than traditional cubic equations of state, especially for systems containing liquids or solids. Most physically based equations of state are built on monomer term describing the
4062:. Cubic equations of state originated from the van der Waals equation of state. Hence, all cubic equations of state can be considered 'modified van der Waals equation of state'. There is a very large number of such cubic equations of state. For process engineering, cubic equations of state are today still highly relevant, e.g. the Peng Robinson equation of state or the Soave Redlich Kwong equation of state.
4260:
5199:
4942:
6033:{\displaystyle a^{\mathrm {residual} }=\sum _{i=1}^{8}\sum _{j=-8}^{12}n_{i,j}\delta ^{i}\tau ^{j/8}+\sum _{i=1}^{5}\sum _{j=-8}^{24}n_{i,j}\delta ^{i}\tau ^{j/8}\exp \left(-\delta \right)+\sum _{i=1}^{5}\sum _{j=16}^{56}n_{i,j}\delta ^{i}\tau ^{j/8}\exp \left(-\delta ^{2}\right)+\sum _{i=2}^{4}\sum _{j=24}^{38}n_{i,j}\delta ^{i}\tau ^{j/2}\exp \left(-\delta ^{3}\right)}
4955:
3682:
4669:
3385:
4601:{\displaystyle p=\rho RT+\left(B_{0}RT-A_{0}-{\frac {C_{0}}{T^{2}}}+{\frac {D_{0}}{T^{3}}}-{\frac {E_{0}}{T^{4}}}\right)\rho ^{2}+\left(bRT-a-{\frac {d}{T}}\right)\rho ^{3}+\alpha \left(a+{\frac {d}{T}}\right)\rho ^{6}+{\frac {c\rho ^{3}}{T^{2}}}\left(1+\gamma \rho ^{2}\right)\exp \left(-\gamma \rho ^{2}\right)}
6957:
5542:
are in most cases the critical values for the pure fluid. Because integration of the multiparameter equations of state is not required and thermodynamic properties can be determined using classical thermodynamic relations, there are few restrictions as to the functional form of the ideal or residual
2092:
was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that
5265:
of
Wertheim) to describe the interactions between molecules in a system. The idea of a SAFT equation of state was first proposed by Chapman et al. in 1988 and 1989. Many different versions of the SAFT models have been proposed, but all use the same chain and association terms derived by Chapman et
5236:
is frequently used for modelling dispersive interactions in an equation of state. There is a large number of perturbation theory based equations of state available today, e.g. for the classical
Lennard-Jones fluid. The two most important theories used for these types of equations of state are the
1830:
An equation used to model this relationship is called an equation of state. In most cases this model will comprise some empirical parameters that are usually adjusted to measurement data. Equations of state can also describe solids, including the transition of solids from one crystalline state to
6276:
under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002
5275:
models is in most parts not physically motivated. They can be usually applied in both liquid and gaseous states. Empirical multiparameter equations of state represent the
Helmholtz energy of the fluid as the sum of ideal gas and residual terms. Both terms are explicit in temperature and density:
5274:
Multiparameter equations of state are empirical equations of state that can be used to represent pure fluids with high accuracy. Multiparameter equations of state are empirical correlations of experimental data and are usually formulated in the
Helmholtz free energy. The functional form of these
4006:, an increase in the value for pressure from its classical value implying an effective repulsion between particles (this is an apparent repulsion due to quantum exchange effects not because of actual interactions between particles since in ideal gas, interactional forces are neglected) and in
5418:
6703:
3468:
3180:
5212:
as a function of temperature, density (and for mixtures additionally the composition). The
Helmholtz energy is formulated as a sum of multiple terms modelling different types of molecular interaction or molecular structures, e.g. the formation of chains or
4204:
6769:
1706:
At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the
4946:
Note that in this virial equation, the fourth and fifth virial terms are zero. The second virial coefficient is monotonically decreasing as temperature is lowered. The third virial coefficient is monotonically increasing as temperature is lowered.
5194:{\displaystyle p={\frac {RT}{V}}\left(1+{\frac {B}{V_{r}}}+{\frac {C}{V_{r}^{2}}}+{\frac {D}{V_{r}^{5}}}+{\frac {c_{4}}{T_{r}^{3}V_{r}^{2}}}\left(\beta +{\frac {\gamma }{V_{r}^{2}}}\right)\exp \left({\frac {-\gamma }{V_{r}^{2}}}\right)\right)}
1711:, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. This equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid.
4937:{\displaystyle p=\rho RT+\left(B_{0}RT-A_{0}-{\frac {C_{0}}{T^{2}}}+{\frac {D_{0}}{T^{3}}}-{\frac {E_{0}}{T^{4}}}\right)\rho ^{2}+\left(bRT-a-{\frac {d}{T}}+{\frac {c}{T^{2}}}\right)\rho ^{3}+\alpha \left(a+{\frac {d}{T}}\right)\rho ^{6}}
8714:
Gil-Villegas, Alejandro; Galindo, Amparo; Whitehead, Paul J.; Mills, Stuart J.; Jackson, George; Burgess, Andrew N. (1997). "Statistical associating fluid theory for chain molecules with attractive potentials of variable range".
2371:
5278:
5484:
2538:
6586:
2653:
2236:
2456:
6267:
4083:
1378:
6352:
6128:
66:. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and
3798:
3741:
6042:
This is a somewhat simpler form that is intended to be used more in technical applications. Equations of state that require a higher accuracy use a more complicated form with more terms.
8352:
Saajanlehto, Meri; Uusi-Kyyny, Petri; Alopaeus, Ville (2014). "A modified continuous flow apparatus for gas solubility measurements at high pressure and temperature with camera system".
8138:"Molecular thermodynamics for fluids at low and high densities. Part II: Phase equilibria for mixtures containing components with large differences in molecular size or potential energy"
3677:{\displaystyle {\frac {N}{V}}={\frac {(2s+1)(mk_{\text{B}}T)^{3/2}}{{\sqrt {2}}\pi ^{2}\hbar ^{3}}}\int _{0}^{\infty }{\frac {z^{1/2}\,\mathrm {d} z}{e^{z-\mu /(k_{\text{B}}T)}\pm 1}}.}
4224:
is the first virial coefficient, which has a constant value of 1 and makes the statement that when volume is large, all fluids behave like ideal gases. The second virial coefficient
2146:
3970:
7274:
are given in such references. These parameters are obtained by fitting the JWL-EOS to experimental results. Typical parameters for some explosives are listed in the table below.
6489:
2548:
derived by the assumption of a finite volume occupied by the constituent molecules. His new formula revolutionized the study of equations of state, and was the starting point of
2943:
2871:
2821:
7000:
3380:{\displaystyle p={\frac {(2s+1){\sqrt {2m^{3}k_{\text{B}}^{5}T^{5}}}}{3\pi ^{2}\hbar ^{3}}}\int _{0}^{\infty }{\frac {z^{3/2}\,\mathrm {d} z}{e^{z-\mu /(k_{\text{B}}T)}\pm 1}}}
1949:
3412:
7308:
6409:
6382:
3459:
1213:
1158:
1103:
3047:
Since for atomic and molecular gases, the classical ideal gas law is well suited in most cases, let us describe the equation of state for elementary particles with mass
1759:
910:
863:
778:
731:
643:
596:
7188:
7027:
6536:
5513:
7371:
2983:
814:
682:
7524:
7495:
7338:
7161:
6170:
2751:
2267:
7245:
6952:{\displaystyle p=A\left(1-{\frac {\omega }{R_{1}V}}\right)\exp(-R_{1}V)+B\left(1-{\frac {\omega }{R_{2}V}}\right)\exp \left(-R_{2}V\right)+{\frac {\omega e_{0}}{V}}}
5257:) in fluids, which can also be applied for modelling chain formation (in the limit of infinite association strength). The SAFT equation of state was developed using
1048:
7474:
7446:
7272:
7215:
7141:
7114:
7047:
6563:
6197:
5540:
4653:
4060:
3037:
3010:
2891:
2070:
2041:
2012:
1922:
6429:
7417:
7394:
4000:
2093:
in the long, open end. Through these experiments, Boyle noted that the gas volume varied inversely with the pressure. In mathematical form, this can be stated as:
9440:
6199:
is another constant, representing the molecular attraction between water molecules. The magnitude of the correction is about 2 gigapascals (20,000 atmospheres).
5423:
547:
7087:
7067:
6509:
6150:
4631:
3173:
3153:
3133:
3113:
3085:
3065:
2696:
2676:
2262:
1975:
1889:
1821:
1801:
1781:
886:
839:
754:
707:
619:
572:
10687:
2461:
4216:
equation. If appropriate assumptions are made about the mathematical form of intermolecular forces, theoretical expressions can be developed for each of the
9221:"Equations of states and scaling rules for molecular solids under strong compression" in "Molecular systems under high pressure" ed. R. Pucci and G. Piccino
2159:
found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to roughly the same extent over the same 80-kelvin interval. This is known today as
6411:
is the second order virial parameter of Morse oscillator and it depends on the parameters of Morse oscillator in addition to the absolute temperature.
4659:
Values of the various parameters can be found in reference materials. The BWR equation of state has also frequently been used for the modelling of the
8660:
Chapman, Walter G.; Jackson, G.; Gubbins, K.E. (11 July 1988). "Phase equilibria of associating fluids: Chain molecules with multiple bonding sites".
2241:(1801) of partial pressure states that the pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone.
4010:, a decrease in pressure from its classical value implying an effective attraction. The quantum nature of this equation is in it dependence on s and
2170:
1688:
8282:
Chapman, Walter G.; Gubbins, K.E.; Jackson, G.; Radosz, M. (1 December 1989). "SAFT: Equation-of-state solution model for associating fluids".
1389:
7775:
Redlich, Otto.; Kwong, J. N. S. (1949-02-01). "On the
Thermodynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions".
8799:"A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa"
1277:
10742:
9433:
8054:
Kontogeorgis, Georgios M.; Michelsen, Michael L.; Folas, Georgios K.; Derawi, Samer; von Solms, Nicolas; Stenby, Erling H. (2006-07-01).
511:
6072:
2569:
10747:
10680:
10170:
8687:
Chapman, Walter G.; Gubbins, K.E.; Jackson, G.; Radosz, M. (1 August 1990). "New
Reference Equation of State for Associating Liquids".
3743:, this equation of state will reduce to that of the classical ideal gas. It can be shown that the above equation of state in the limit
5413:{\displaystyle {\frac {a(T,\rho )}{RT}}={\frac {a^{\mathrm {ideal\,gas} }(\tau ,\delta )+a^{\textrm {residual}}(\tau ,\delta )}{RT}}}
4950:
The LeeâKesler equation of state is based on the corresponding states principle, and is a modification of the BWR equation of state.
4208:
Although usually not the most convenient equation of state, the virial equation is important because it can be derived directly from
1367:
8011:
Lee, Byung Ik; Kesler, Michael G. (1975). "A generalized thermodynamic correlation based on three-parameter corresponding states".
2412:
1400:
6698:{\displaystyle pV_{m}=RT~{\frac {\operatorname {Li} _{\alpha +1}(z)}{\zeta (\alpha )}}\left({\frac {T}{T_{c}}}\right)^{\alpha }}
9426:
8325:
Gross, Joachim; Sadowski, Gabriele (2002). "Application of the
Perturbed-Chain SAFT Equation of State to Associating Systems".
2409:. However, later work revealed that the number should actually be closer to 273.2, and then the Celsius scale was defined with
7673:
10673:
9379:
7744:
7654:
6205:
6060:
2096:
970:
3805:
8757:"Equations of State for Technical Applications. I. Simultaneously Optimized Functional Forms for Nonpolar and Polar Fluids"
6298:
5246:
4253:
1681:
1268:
937:
504:
382:
6446:
11042:
2832:
2553:
320:
8849:"The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use"
8056:"Ten Years with the CPA (Cubic-Plus-Association) Equation of State. Part 1. Pure Compounds and Self-Associating Systems"
2758:
9730:
9041:"Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms"
7668:
1452:
1426:
947:
401:
1831:
another. Equations of state are also used for the modeling of the state of matter in the interior of stars, including
9143:
353:
9356:
5208:
There is a large number of physically based equations of state available today. Most of those are formulated in the
4232:
to triplets, and so on. Accuracy can be increased indefinitely by considering higher order terms. The coefficients
7705:
3746:
3689:
1505:
976:
375:
11047:
10437:
9701:
7678:
1674:
1717:
10941:
10507:
10432:
10163:
10114:
9802:
7875:
6284:
of water but few simple alternatives are available for severely nonisentropic processes such as strong shocks.
4199:{\displaystyle {\frac {pV_{m}}{RT}}=A+{\frac {B}{V_{m}}}+{\frac {C}{V_{m}^{2}}}+{\frac {D}{V_{m}^{3}}}+\cdots }
1605:
137:
8093:
Kontogeorgis, Georgios M.; Voutsas, Epaminondas C.; Yakoumis, Iakovos V.; Tassios, Dimitrios P. (1996-01-01).
4666:
The
BenedictâWebbâRubinâStarling equation of state is a modified BWR equation of state and can be written as
1500:
11062:
11037:
10619:
10447:
9547:
2718:
1857:
1843:
1827:, that is, the number of independent variables depends on the number of substances and phases in the system.
1580:
1353:
330:
20:
1823:
the temperature of the system. Yet also other variables may be used in that form. It is directly related to
10710:
10629:
10502:
10247:
9749:
9657:
6755:
3092:
965:
168:
158:
8797:
Span, Roland; Lemmon, Eric W.; Jacobsen, Richard T; Wagner, Wolfgang; Yokozeki, Akimichi (November 2000).
2167:
published results of similar experiments, indicating a linear relationship between volume and temperature:
11057:
9870:
9581:
9515:
7649:
2900:
173:
163:
6766:
The equation of state from JonesâWilkinsâLee is used to describe the detonation products of explosives.
10818:
10734:
8191:
Weingerl, Ulrike; Wendland, Martin; Fischer, Johann; MĂŒller, Andreas; Winkelmann, Jochen (March 2001).
6964:
3088:
2152:
and is sometimes referred to as
Mariotte's law. However, Mariotte's work was not published until 1676.
1457:
1421:
199:
133:
9001:
2084:
was one of the earliest formulation of an equation of state. In 1662, the Irish physicist and chemist
1495:
10156:
9598:
9002:"Ălaboration des lois d'Ă©tat d'un liquide et de sa vapeur pour les modĂšles d'Ă©coulements diphasiques"
7683:
1861:
1250:
998:
444:
257:
247:
3087:
that takes into account quantum effects. In the following, the upper sign will always correspond to
1927:
11052:
10994:
10977:
10654:
10553:
10183:
10029:
10024:
9907:
9875:
9790:
9530:
9520:
7599:
4663:. There are several extensions and modifications of the classical BWR equation of state available.
4028:
4023:
2549:
3390:
10841:
10831:
10757:
10548:
10089:
9770:
9686:
9576:
9366:. NATO Science Series. Vol. 140. Dordrecht, Netherlands: Kluver Academic. pp. 217â236.
8458:
8380:
7950:
7911:
7867:
7285:
6440:
6387:
6360:
5218:
3421:
2164:
1662:
1490:
1287:
1168:
1113:
1058:
990:
929:
465:
454:
120:
55:
43:
8953:"Applications of the IAPWS-95 formulation in fluid inclusion and mineral-fluid phase equilibria"
7818:
Soave, Giorgio (1972). "Equilibrium constants from a modified Redlich-Kwong equation of state".
2088:
performed a series of experiments employing a J-shaped glass tube, which was sealed on one end.
892:
845:
760:
713:
625:
578:
24:
10888:
10573:
10563:
10313:
10308:
9669:
9542:
9401:
S. Benjelloun, "Thermodynamic identities and thermodynamic consistency of Equation of States",
7166:
7005:
6514:
6281:
5491:
4213:
2545:
1836:
1595:
1312:
396:
150:
125:
7345:
2952:
1515:
796:
661:
10773:
10696:
10074:
9652:
7501:
7480:
7315:
7146:
6742:
6155:
5258:
5250:
5209:
4209:
1530:
1107:
420:
266:
115:
9133:
8231:
8192:
8137:
7220:
1018:
10916:
10492:
10252:
10137:
9811:
9715:
9710:
9681:
9647:
9627:
9612:
9593:
9564:
9505:
9321:
9270:
9178:
9052:
8964:
8899:
8810:
8724:
8595:
8548:
8501:
8423:
8243:
8204:
8149:
8020:
7962:
7827:
7452:
7424:
7250:
7193:
7119:
7092:
7032:
6711:
is an exponent specific to the system (e.g. in the absence of a potential field, α = 3/2),
6541:
6175:
6056:
5518:
4638:
4038:
3015:
2988:
2876:
2048:
2019:
1990:
1900:
1610:
1535:
1525:
325:
187:
8490:"Perturbation Theory and Equation of State for Fluids. II. A Successful Theory of Liquids"
8459:"A child of prediction. On the History, Ontology, and Computation of the Lennard-Jonesium"
7852:
Landau, L. D., Lifshitz, E. M. (1980). Statistical physics: Part I (Vol. 5). page 162-166.
6414:
6292:
An equation of state of Morse oscillator has been derived, and it has the following form:
5237:
Barker-Henderson perturbation theory and the WeeksâChandlerâAndersen perturbation theory.
8:
10982:
10961:
10467:
10359:
10349:
10262:
10217:
10109:
9961:
9900:
9880:
9696:
9642:
9525:
9484:
9450:
7401:
7378:
5262:
5233:
4660:
3977:
2946:
2541:
1850:
1555:
1317:
339:
305:
300:
213:
9325:
9274:
9182:
9056:
8968:
8903:
8814:
8728:
8599:
8552:
8505:
8427:
8247:
8208:
8153:
8024:
7966:
7831:
1550:
529:
11009:
10921:
10898:
10879:
10859:
10823:
10614:
10543:
10377:
9780:
9775:
9559:
9294:
9194:
9083:
9040:
9017:
8928:
8887:
8776:
8619:
8307:
8173:
7931:
7700:
7072:
7052:
6734:
6494:
6135:
4616:
4217:
3462:
3415:
3158:
3138:
3118:
3098:
3070:
3050:
2681:
2661:
2247:
1960:
1874:
1806:
1786:
1766:
1644:
1307:
1302:
1255:
871:
824:
739:
692:
604:
557:
487:
471:
358:
310:
295:
285:
94:
88:
50:, which describe the state of matter under a given set of physical conditions, such as
9674:
2374:
11014:
10911:
10884:
10795:
10785:
10778:
10644:
10639:
10568:
10457:
10409:
10394:
10287:
10257:
9828:
9765:
9744:
9739:
9632:
9375:
9337:
9298:
9286:
9282:
9198:
9139:
9108:"LLNL Explosives Handbook: Properties of Chemical Explosives and Explosive Simulants"
9088:
9070:
9021:
8982:
8933:
8915:
8868:
8826:
8780:
8623:
8611:
8564:
8537:"Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids"
8517:
8439:
8299:
8295:
8259:
8165:
8114:
8075:
8036:
7978:
7935:
7889:
7881:
7871:
7839:
7800:
7792:
7740:
7715:
2089:
1639:
1600:
1590:
1162:
960:
788:
290:
280:
8311:
8177:
6761:
6202:
The equation is stated in this form because the speed of sound in water is given by
10906:
10599:
10222:
10064:
9973:
9966:
9956:
9932:
9797:
9367:
9329:
9278:
9243:
9234:
Holzapfel, W.B. (1991) . "Equations of state for solids under strong compression".
9186:
9078:
9060:
9013:
8972:
8923:
8907:
8860:
8818:
8768:
8756:
8732:
8696:
8669:
8642:
Chapman, Walter G. (1988). "Theory and Simulation of Associating Liquid Mixtures".
8603:
8556:
8509:
8470:
8431:
8411:
8392:
8361:
8334:
8291:
8251:
8212:
8157:
8106:
8067:
8028:
7970:
7923:
7835:
7784:
6064:
4076:
2829:
gas approximation is used, then the ideal gas law may also be expressed as follows
2160:
1560:
1545:
1485:
1480:
1297:
1292:
942:
410:
275:
16:
An equation describing the state of matter under a given set of physical conditions
10956:
9166:
9065:
5546:
One example of such an equation of state is the form proposed by Span and Wagner.
10951:
10946:
10874:
10869:
10836:
10763:
10589:
10442:
10179:
10079:
10014:
9991:
9927:
9912:
9895:
9845:
9833:
9720:
9691:
9608:
9586:
9569:
9535:
9469:
9464:
9405:
9371:
9312:
Holzapfel, W.B. (1998). "Equation of state for solids under strong compression".
8848:
8798:
8584:"Fluids with highly directional attractive forces. I. Statistical thermodynamics"
8536:
8489:
7531:
2238:
2156:
1510:
1358:
1012:
653:
476:
237:
204:
63:
9418:
8474:
8396:
8381:"Equation of state for the LennardâJones fluid based on the perturbation theory"
8365:
7927:
2366:{\displaystyle p_{\text{total}}=p_{1}+p_{2}+\cdots +p_{n}=\sum _{i=1}^{n}p_{i}.}
10999:
10715:
10387:
10382:
10339:
10272:
10267:
10084:
9951:
9865:
9823:
9637:
8911:
8133:
7163:
are given by several references. In addition, the initial density (solid part)
6566:
4032:
2894:
2081:
1565:
1335:
435:
315:
252:
242:
110:
80:
47:
9333:
9247:
8977:
8952:
8772:
8673:
7974:
11031:
10987:
10624:
10604:
10527:
10487:
10422:
10354:
10277:
10132:
10099:
9996:
9860:
9725:
9341:
9290:
9074:
9025:
8986:
8919:
8872:
8830:
8615:
8568:
8521:
8443:
8303:
8263:
8169:
8118:
8094:
8079:
8055:
8040:
7982:
7796:
7639:
7565:
6738:
5254:
5222:
5214:
2712:
2379:
2149:
1840:
1708:
1634:
952:
521:
482:
194:
8435:
8193:"Backone family of equations of state: 2. Nonpolar and polar fluid mixtures"
11004:
10649:
10522:
10517:
10512:
10477:
10427:
10344:
10104:
10094:
10069:
9357:"Equations of State and Thermophysical Properties of Solids Under Pressure"
9092:
8937:
8379:
Betancourt-CĂĄrdenas, F.F.; Galicia-Luna, L.A.; Sandler, S.I. (March 2008).
7804:
6172:
is an empirically determined constant typically taken to be about 6.1, and
5479:{\displaystyle \tau ={\frac {T_{r}}{T}},\delta ={\frac {\rho }{\rho _{r}}}}
2406:
2085:
1978:
1952:
1832:
1585:
1570:
1520:
1003:
10148:
8888:"Unphysical Critical Curves of Binary Mixtures Predicted with GERG Models"
8255:
8216:
8161:
8032:
7893:
7762:
On the Continuity of the Gaseous and Liquid States (doctoral dissertation)
10813:
10808:
10558:
10452:
10364:
10019:
9107:
8232:"Backone family of equations of state: 1. Nonpolar and polar pure fluids"
7949:
Nicolas, J.J.; Gubbins, K.E.; Streett, W.B.; Tildesley, D.J. (May 1979).
7912:"Review and comparison of equations of state for the Lennard-Jones fluid"
5245:
An important contribution for physically based equations of state is the
2826:
2533:{\displaystyle pV_{m}=R\left(T_{C}+273.15\ {}^{\circ }{\text{C}}\right).}
1892:
1540:
348:
59:
10665:
8700:
8583:
7788:
6055:
When considering water under very high pressures, in situations such as
10803:
10497:
10472:
10399:
10369:
10303:
10282:
10034:
9946:
9785:
9479:
9261:
Holzapfel, Wi.B. (1996). "Physics of solids under strong compression".
9190:
8607:
7642:
for water and other liquids. Several equations are referred to as the
6384:
is the first order virial parameter and it depends on the temperature,
2985:
is the internal energy per unit mass (the "specific internal energy"),
1824:
1629:
1575:
8864:
8822:
8560:
8513:
8378:
8338:
8110:
8071:
2678:
is a parameter describing the attractive energy between particles and
2377:
combined Boyle's law and Charles' law into the first statement of the
10864:
10056:
10046:
10041:
9983:
9890:
9474:
8736:
4003:
227:
35:
10232:
10768:
10634:
10462:
10006:
9917:
9885:
9510:
9402:
8230:
MĂŒller, Andreas; Winkelmann, Jochen; Fischer, Johann (April 1996).
7710:
7695:
6578:
4007:
1343:
1260:
1052:
460:
232:
51:
8092:
7811:
7049:, which is the density of the detonation products. The parameters
2648:{\displaystyle \left(P+a{\frac {1}{V_{m}^{2}}}\right)(V_{m}-b)=RT}
10933:
10594:
10482:
10417:
10334:
10329:
9818:
9758:
8713:
8535:
Weeks, John D.; Chandler, David; Andersen, Hans C. (1971-06-15).
6762:
JonesâWilkinsâLee equation of state for explosives (JWL equation)
449:
31:
9167:"Finite strain theories and comparisons with seismological data"
8457:
Lenhard, Johannes; Stephan, Simon; Hasse, Hans (February 2024).
8053:
7885:
10203:
9922:
1865:
7948:
5240:
2401:+ 267) (with temperature expressed in degrees Celsius), where
2231:{\displaystyle {\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}.}
10212:
10198:
10124:
9853:
9620:
8351:
8190:
7910:
Stephan, Simon; Staubach, Jens; Hasse, Hans (November 2020).
67:
23:. For the use of this concept in optimal control theory, see
9105:
8686:
8281:
2451:{\displaystyle 0~^{\circ }\mathrm {C} =273.15~\mathrm {K} }
1853:
and petroleum industry as well as pharmaceutical industry.
1714:
The general form of an equation of state may be written as
425:
71:
10208:
9939:
7247:
and the chemical energy per unit volume of the explosive
7029:, which is the density of the explosive (solid part) and
70:
states as well as the state of matter in the interior of
8796:
6272:
Thus water behaves as though it is an ideal gas that is
4228:
corresponds to interactions between pairs of molecules,
2897:
of the gas (number of atoms/molecules per unit volume),
2698:
is a parameter describing the volume of the particles.
2557:
8999:
8229:
6262:{\displaystyle c^{2}=\gamma \left(p+p^{0}\right)/\rho }
2755:
In the form shown above, the equation of state is thus
8412:"Perturbation Theory and Equation of State for Fluids"
6434:
5203:
3012:
is the specific heat capacity at constant volume, and
2563:
The van der Waals equation of state can be written as
1849:
Equations of state are applied in many fields such as
8659:
8655:
8653:
8534:
8277:
8275:
8273:
7504:
7483:
7455:
7427:
7404:
7381:
7348:
7318:
7288:
7253:
7223:
7196:
7169:
7149:
7122:
7095:
7075:
7055:
7035:
7008:
6967:
6772:
6589:
6544:
6517:
6497:
6449:
6417:
6390:
6363:
6347:{\displaystyle p=\Gamma _{1}\nu +\Gamma _{2}\nu ^{2}}
6301:
6287:
6208:
6178:
6158:
6138:
6075:
6045:
5554:
5521:
5494:
5426:
5281:
4958:
4672:
4641:
4619:
4263:
4086:
4041:
3980:
3808:
3749:
3692:
3471:
3424:
3393:
3183:
3161:
3141:
3121:
3101:
3073:
3053:
3018:
2991:
2955:
2903:
2879:
2835:
2761:
2721:
2684:
2664:
2572:
2464:
2415:
2270:
2250:
2173:
2099:
2051:
2022:
1993:
1963:
1930:
1903:
1877:
1809:
1789:
1769:
1720:
1171:
1116:
1061:
1021:
895:
874:
848:
827:
799:
763:
742:
716:
695:
664:
628:
607:
581:
560:
532:
7909:
5269:
3039:
is the specific heat capacity at constant pressure.
9165:Stacey, F.D.; Brennan, B. J.; Irvine, R.D. (1981).
9164:
9000:Le MĂ©tayer, O; Massoni, J; Saurel, R (2004-03-01).
8456:
5228:
4031:are called such because they can be rewritten as a
2148:The above relationship has also been attributed to
8886:Deiters, Ulrich K.; Bell, Ian H. (December 2020).
8680:
8650:
8270:
8131:
7759:
7518:
7489:
7468:
7440:
7411:
7388:
7365:
7332:
7302:
7266:
7239:
7209:
7182:
7155:
7135:
7108:
7081:
7061:
7041:
7021:
6994:
6951:
6697:
6557:
6530:
6503:
6483:
6423:
6403:
6376:
6346:
6277:atmospheres (2000.1 MPa to 2000.2 MPa).
6261:
6191:
6164:
6144:
6123:{\displaystyle p=\rho (\gamma -1)e-\gamma p^{0}\,}
6122:
6032:
5534:
5507:
5478:
5412:
5193:
4936:
4647:
4625:
4600:
4198:
4054:
3994:
3964:
3792:
3735:
3676:
3453:
3406:
3379:
3167:
3147:
3127:
3107:
3079:
3059:
3031:
3004:
2977:
2937:
2885:
2865:
2815:
2745:
2690:
2670:
2647:
2532:
2450:
2365:
2256:
2230:
2140:
2064:
2035:
2006:
1969:
1943:
1916:
1883:
1856:Any consistent set of units may be used, although
1815:
1795:
1775:
1753:
1207:
1152:
1097:
1042:
904:
880:
857:
833:
808:
772:
748:
725:
701:
676:
637:
613:
590:
566:
541:
9448:
9158:
6067:, the stiffened equation of state is often used:
1839:) and radiation fields. A related concept is the
11029:
8410:Levesque, Dominique; Verlet, Loup (1969-06-05).
7905:
7903:
8853:Journal of Physical and Chemical Reference Data
8803:Journal of Physical and Chemical Reference Data
8487:
8327:Industrial & Engineering Chemistry Research
8099:Industrial & Engineering Chemistry Research
8060:Industrial & Engineering Chemistry Research
7951:"Equation of state for the Lennard-Jones fluid"
6572:
8637:
8635:
8633:
8488:Barker, J. A.; Henderson, D. (December 1967).
8409:
7734:
6050:
10681:
10164:
9434:
9305:
9254:
8324:
8095:"An Equation of State for Associating Fluids"
7900:
7861:
3793:{\displaystyle e^{\mu /(k_{\text{B}}T)}\ll 1}
3736:{\displaystyle e^{\mu /(k_{\text{B}}T)}\ll 1}
1682:
8463:Studies in History and Philosophy of Science
7998:Fluid Properties for Light Petroleum Systems
7864:Fluid Properties for Light Petroleum Systems
7774:
7753:
4247:
4065:
3465:is given by the following implicit function
2244:Mathematically, this can be represented for
2072:, absolute temperature at the critical point
10178:
8885:
8630:
5241:Statistical associating fluid theory (SAFT)
4070:
4017:
3095:. The equation of state of such gases with
10688:
10674:
10171:
10157:
9441:
9427:
9395:
9223:. North-Holland: Elsevier. pp. 61â68.
8846:
8754:
4244:, etc. are functions of temperature only.
2706:
1689:
1675:
87:
10695:
9362:. In Katrusiak, A.; McMillan, P. (eds.).
9354:
9311:
9260:
9233:
9218:
9082:
9064:
9006:International Journal of Thermal Sciences
8976:
8927:
8644:Doctoral Dissertation, Cornell University
8010:
7515:
7408:
7385:
7362:
7329:
7299:
6119:
5341:
3611:
3317:
9135:Computer Simulation of Dynamic Phenomena
9038:
8581:
7995:
6431:is the fractional volume of the system.
3042:
2552:, which most famously continued via the
2076:
9131:
9125:
9099:
8641:
8000:. Gulf Publishing Company. p. 270.
7659:StaceyâBrennanâIrvine equation of state
6754:is the critical temperature at which a
5253:that describes the association (a.k.a.
4002:, decreasing the temperature causes in
2383:. Initially, the law was formulated as
2141:{\displaystyle pV=\mathrm {constant} .}
1955:, the volume of 1 mole of gas or liquid
11030:
9106:B. M. Dobratz; P. C. Crawford (1985).
8951:Shi, Lanlan; Mao, Shide (2012-01-01).
8950:
8892:International Journal of Thermophysics
8761:International Journal of Thermophysics
6152:is the internal energy per unit mass,
3965:{\displaystyle pV=Nk_{\text{B}}T\left}
19:For the use of this in cosmology, see
10669:
10152:
9422:
8842:
8840:
8792:
8790:
8750:
8748:
8746:
7817:
7728:
25:Optimal control § General method
7665:Adapted polynomial equation of state
6484:{\displaystyle p=\rho _{m}c_{s}^{2}}
5247:statistical associating fluid theory
2043:, molar volume at the critical point
1868:(K), with zero being absolute zero.
7669:JohnsonâHolmquist equation of state
6577:The equation of state for an ideal
6435:Ultrarelativistic equation of state
5204:Physically based equations of state
4212:. This equation is also called the
2945:is the (constant) adiabatic index (
2938:{\displaystyle \gamma =C_{p}/C_{v}}
2866:{\displaystyle p=\rho (\gamma -1)e}
2558:Soave modification of Redlich-Kwong
1844:equation of state used in cosmology
13:
9018:10.1016/j.ijthermalsci.2003.09.002
8847:Wagner, W.; PruĂ, A. (June 2002).
8837:
8787:
8743:
7662:Modified Rydberg equation of state
6392:
6365:
6325:
6309:
6288:Morse oscillator equation of state
6046:List of further equations of state
5582:
5579:
5576:
5573:
5570:
5567:
5564:
5561:
5348:
5345:
5342:
5338:
5335:
5332:
5329:
5326:
3613:
3585:
3319:
3291:
2816:{\displaystyle f(p,V,T)=pV-nRT=0.}
2444:
2430:
2131:
2128:
2125:
2122:
2119:
2116:
2113:
2110:
896:
849:
764:
717:
629:
582:
402:Intensive and extensive properties
14:
11074:
9414:
7768:
7655:BirchâMurnaghan equation of state
6995:{\displaystyle V=\rho _{e}/\rho }
5270:Multiparameter equations of state
10724:
10231:
7706:Table of thermodynamic equations
5229:Perturbation theory-based models
2701:
2014:, pressure at the critical point
1658:
1657:
977:Table of thermodynamic equations
9355:Holzapfel, Wilfried B. (2004).
9348:
9227:
9212:
9039:Al-Raeei, Marwan (2022-04-01).
9032:
8993:
8944:
8879:
8717:The Journal of Chemical Physics
8707:
8575:
8541:The Journal of Chemical Physics
8528:
8494:The Journal of Chemical Physics
8481:
8450:
8403:
8372:
8345:
8318:
8223:
8184:
8125:
8086:
8047:
8004:
7679:Anton-Schmidt equation of state
7674:MieâGrĂŒneisen equation of state
2554:RedlichâKwong equation of state
1453:Maxwell's thermodynamic surface
8588:Journal of Statistical Physics
8582:Wertheim, M. S. (April 1984).
7989:
7942:
7855:
7846:
6845:
6826:
6657:
6651:
6643:
6637:
6280:This equation mispredicts the
6097:
6085:
5396:
5384:
5366:
5354:
5300:
5288:
3931:
3911:
3884:
3869:
3779:
3763:
3722:
3706:
3657:
3641:
3526:
3506:
3503:
3488:
3448:
3428:
3363:
3347:
3208:
3193:
2857:
2845:
2783:
2765:
2633:
2614:
1944:{\displaystyle {\frac {V}{n}}}
1742:
1724:
1187:
1175:
1132:
1120:
1077:
1065:
1037:
1025:
1:
10620:Macroscopic quantum phenomena
9364:High-Pressure Crystallography
9066:10.1016/j.heliyon.2022.e09328
8755:Span, R.; Wagner, W. (2003).
7996:Starling, Kenneth E. (1973).
7760:van der Waals; J. D. (1873).
7721:
6057:underwater nuclear explosions
3115:particles occupying a volume
2155:In 1787 the French physicist
1354:Mechanical equivalent of heat
21:Equation of state (cosmology)
10711:Principle of maximum entropy
10630:Order and disorder (physics)
9372:10.1007/978-1-4020-2102-2_14
8296:10.1016/0378-3812(89)80308-5
7840:10.1016/0009-2509(72)80096-4
7820:Chemical Engineering Science
6573:Ideal Bose equation of state
5249:(SAFT) that contributes the
4254:BenedictâWebbâRubin equation
3974:With a fixed number density
3407:{\displaystyle k_{\text{B}}}
966:Onsager reciprocal relations
7:
8475:10.1016/j.shpsa.2023.11.007
8397:10.1016/j.fluid.2007.11.015
8366:10.1016/j.fluid.2014.08.035
7928:10.1016/j.fluid.2020.112772
7739:. Oxford University Press.
7689:
7650:Murnaghan equation of state
7303:{\displaystyle \rho _{e}\,}
7217:, ChapmanâJouguet pressure
6404:{\displaystyle \Gamma _{2}}
6377:{\displaystyle \Gamma _{1}}
6051:Stiffened equation of state
5261:methods (in particular the
3686:In the limiting case where
3454:{\displaystyle \mu (T,N/V)}
1701:
1458:Entropy as energy dispersal
1269:"Perpetual motion" machines
1208:{\displaystyle G(T,p)=H-TS}
1153:{\displaystyle A(T,V)=U-TS}
1098:{\displaystyle H(S,p)=U+pV}
10:
11079:
11043:Engineering thermodynamics
10735:Statistical thermodynamics
9283:10.1088/0034-4885/59/1/002
8912:10.1007/s10765-020-02743-3
4251:
4074:
4021:
1754:{\displaystyle f(p,V,T)=0}
905:{\displaystyle \partial T}
858:{\displaystyle \partial V}
773:{\displaystyle \partial p}
726:{\displaystyle \partial V}
638:{\displaystyle \partial T}
591:{\displaystyle \partial S}
18:
10970:
10932:
10897:
10852:
10794:
10733:
10722:
10703:
10582:
10536:
10408:
10322:
10296:
10240:
10229:
10191:
10123:
10055:
10005:
9982:
9844:
9607:
9493:
9457:
9334:10.1080/08957959808200283
9248:10.1080/08957959108245571
9132:Wilkins, Mark L. (1999),
8978:10.1016/j.gsf.2011.08.002
8674:10.1080/00268978800101601
7975:10.1080/00268977900101051
7684:State-transition equation
7633:
7183:{\displaystyle \rho _{0}}
7022:{\displaystyle \rho _{e}}
6538:is the mass density, and
6531:{\displaystyle \rho _{m}}
5508:{\displaystyle \rho _{r}}
4248:The BWR equation of state
4066:Virial equations of state
1864:refers to the use of the
1379:An Inquiry Concerning the
10995:Condensed matter physics
10978:Statistical field theory
10655:Thermo-dielectric effect
10554:Enthalpy of vaporization
10248:BoseâEinstein condensate
9791:Compact tension specimen
9511:Conservation of momentum
9219:Holzapfel, W.B. (1991).
9138:, Springer, p. 80,
7737:A to Z of Thermodynamics
7366:{\displaystyle p_{CJ}\,}
6756:BoseâEinstein condensate
5515:and reduced temperature
4071:Virial equation of state
4029:Cubic equations of state
4024:Cubic equations of state
4018:Cubic equations of state
3093:BoseâEinstein statistics
2978:{\displaystyle e=C_{v}T}
2550:cubic equations of state
1392:Heterogeneous Substances
809:{\displaystyle \alpha =}
677:{\displaystyle \beta =-}
10853:Mathematical approaches
10842:Lennard-Jones potential
10758:thermodynamic potential
10549:Enthalpy of sublimation
9871:NavierâStokes equations
9771:Material failure theory
9759:Material failure theory
8773:10.1023/A:1022390430888
8436:10.1103/PhysRev.182.307
7868:Gulf Publishing Company
7735:Perrot, Pierre (1998).
7519:{\displaystyle e_{0}\,}
7490:{\displaystyle \omega }
7333:{\displaystyle v_{D}\,}
7156:{\displaystyle \omega }
6441:ultrarelativistic fluid
6165:{\displaystyle \gamma }
6061:sonic shock lithotripsy
2947:ratio of specific heats
2746:{\displaystyle pV=nRT.}
2707:Classical ideal gas law
2165:Joseph Louis Gay-Lussac
11048:Mechanical engineering
10889:conformal field theory
10564:Latent internal energy
10314:Color-glass condensate
9543:Conservation of energy
9403:Link to Archiv e-print
8385:Fluid Phase Equilibria
8354:Fluid Phase Equilibria
8284:Fluid Phase Equilibria
7916:Fluid Phase Equilibria
7862:K.E. Starling (1973).
7764:. Universiteit Leiden.
7520:
7491:
7470:
7442:
7413:
7390:
7367:
7334:
7304:
7268:
7241:
7240:{\displaystyle P_{CJ}}
7211:
7190:, speed of detonation
7184:
7157:
7137:
7110:
7083:
7063:
7043:
7023:
6996:
6953:
6699:
6559:
6532:
6505:
6485:
6443:has equation of state
6425:
6405:
6378:
6348:
6282:specific heat capacity
6263:
6193:
6166:
6146:
6124:
6034:
5956:
5935:
5838:
5817:
5727:
5703:
5635:
5611:
5536:
5509:
5480:
5414:
5259:statistical mechanical
5195:
4938:
4649:
4627:
4602:
4200:
4056:
3996:
3966:
3794:
3737:
3678:
3455:
3408:
3381:
3169:
3149:
3129:
3109:
3091:and the lower sign to
3089:FermiâDirac statistics
3081:
3061:
3033:
3006:
2979:
2939:
2887:
2867:
2817:
2747:
2692:
2672:
2649:
2534:
2452:
2367:
2349:
2258:
2232:
2142:
2066:
2037:
2008:
1971:
1945:
1918:
1885:
1817:
1797:
1777:
1755:
1209:
1154:
1099:
1044:
1043:{\displaystyle U(S,V)}
906:
882:
859:
835:
810:
774:
750:
727:
703:
678:
639:
615:
592:
568:
543:
522:Specific heat capacity
126:Quantum thermodynamics
44:thermodynamic equation
10804:Ferromagnetism models
10697:Statistical mechanics
10374:Magnetically ordered
9908:Archimedes' principle
9876:Bernoulli's principle
9171:Surveys in Geophysics
8256:10.1002/aic.690420423
8217:10.1002/aic.690470317
8162:10.1002/aic.690321105
8033:10.1002/aic.690210313
7521:
7492:
7471:
7469:{\displaystyle R_{2}}
7443:
7441:{\displaystyle R_{1}}
7414:
7391:
7368:
7335:
7305:
7269:
7267:{\displaystyle e_{0}}
7242:
7212:
7210:{\displaystyle V_{D}}
7185:
7158:
7138:
7136:{\displaystyle R_{2}}
7111:
7109:{\displaystyle R_{1}}
7084:
7064:
7044:
7042:{\displaystyle \rho }
7024:
6997:
6954:
6743:Riemann zeta function
6700:
6560:
6558:{\displaystyle c_{s}}
6533:
6506:
6486:
6426:
6406:
6379:
6349:
6264:
6194:
6192:{\displaystyle p^{0}}
6167:
6147:
6125:
6035:
5936:
5915:
5818:
5797:
5704:
5683:
5612:
5591:
5537:
5535:{\displaystyle T_{r}}
5510:
5481:
5415:
5210:Helmholtz free energy
5196:
4939:
4650:
4648:{\displaystyle \rho }
4628:
4603:
4210:statistical mechanics
4201:
4057:
4055:{\displaystyle V_{m}}
3997:
3967:
3795:
3738:
3679:
3456:
3409:
3382:
3170:
3150:
3130:
3110:
3082:
3062:
3043:Quantum ideal gas law
3034:
3032:{\displaystyle C_{p}}
3007:
3005:{\displaystyle C_{v}}
2980:
2940:
2888:
2886:{\displaystyle \rho }
2868:
2818:
2748:
2693:
2673:
2650:
2544:introduced the first
2535:
2453:
2368:
2329:
2259:
2233:
2143:
2077:Historical background
2067:
2065:{\displaystyle T_{c}}
2038:
2036:{\displaystyle V_{c}}
2009:
2007:{\displaystyle p_{c}}
1972:
1946:
1919:
1917:{\displaystyle V_{m}}
1886:
1860:units are preferred.
1818:
1798:
1778:
1756:
1390:On the Equilibrium of
1210:
1155:
1108:Helmholtz free energy
1100:
1045:
907:
883:
860:
836:
811:
775:
751:
728:
704:
679:
640:
616:
593:
569:
544:
11063:Thermodynamic models
11038:Equations of physics
10253:Fermionic condensate
10138:William Prager Medal
9716:Rock mass plasticity
9613:Structural mechanics
9506:Conservation of mass
9494:Laws and Definitions
8957:Geoscience Frontiers
7502:
7481:
7453:
7425:
7402:
7379:
7346:
7316:
7286:
7251:
7221:
7194:
7167:
7147:
7120:
7093:
7073:
7053:
7033:
7006:
7002:is defined by using
6965:
6770:
6587:
6542:
6515:
6495:
6447:
6424:{\displaystyle \nu }
6415:
6388:
6361:
6299:
6206:
6176:
6156:
6136:
6073:
5552:
5519:
5492:
5488:The reduced density
5424:
5279:
5215:dipolar interactions
4956:
4670:
4639:
4617:
4261:
4084:
4039:
3978:
3806:
3747:
3690:
3469:
3422:
3391:
3181:
3159:
3139:
3119:
3099:
3071:
3051:
3016:
2989:
2953:
2901:
2877:
2833:
2759:
2719:
2682:
2662:
2570:
2462:
2413:
2268:
2248:
2171:
2097:
2049:
2020:
1991:
1961:
1928:
1901:
1875:
1862:Absolute temperature
1807:
1787:
1767:
1718:
1403:Motive Power of Fire
1169:
1114:
1059:
1019:
971:Bridgman's equations
948:Fundamental relation
893:
872:
846:
825:
797:
761:
740:
714:
693:
662:
626:
605:
579:
558:
530:
10983:elementary particle
10748:partition functions
10468:Chemical ionization
10360:Programmable matter
10350:Quantum spin liquid
10218:Supercritical fluid
9881:Poiseuille equation
9658:Membrane elasticity
9643:Transverse isotropy
9485:Rigid body dynamics
9451:continuum mechanics
9406:Link to Hal e-print
9326:1998HPR....16...81H
9275:1996RPPh...59...29H
9183:1981GeoSu...4..189S
9057:2022Heliy...809328A
8969:2012GeoFr...3...51S
8904:2020IJT....41..169D
8815:2000JPCRD..29.1361S
8729:1997JChPh.106.4168G
8701:10.1021/ie00104a021
8689:Ind. Eng. Chem. Res
8600:1984JSP....35...19W
8553:1971JChPh..54.5237W
8506:1967JChPh..47.4714B
8428:1969PhRv..182..307L
8248:1996AIChE..42.1116M
8209:2001AIChE..47..705W
8154:1986AIChE..32.1799C
8025:1975AIChE..21..510L
7967:1979MolPh..37.1429N
7832:1972ChEnS..27.1197S
7789:10.1021/cr60137a013
7412:{\displaystyle B\,}
7389:{\displaystyle A\,}
6480:
5263:perturbation theory
5234:Perturbation theory
5219:Lennard-Jones fluid
5179:
5137:
5103:
5088:
5055:
5030:
4661:Lennard-Jones fluid
4187:
4162:
3995:{\displaystyle N/V}
3589:
3295:
3240:
2827:calorically perfect
2606:
2542:J. D. van der Waals
1851:process engineering
1837:quarkâgluon plasmas
1381:Source ... Friction
1313:Loschmidt's paradox
505:Material properties
383:Conjugate variables
11058:Equations of state
11010:information theory
10917:correlation length
10912:Critical exponents
10899:Critical phenomena
10880:stochastic process
10860:Boltzmann equation
10753:equations of state
10615:Leidenfrost effect
10544:Enthalpy of fusion
10309:Quarkâgluon plasma
10030:Electrorheological
10025:Magnetorheological
9781:Fracture mechanics
9548:Entropy inequality
9191:10.1007/BF01449185
8608:10.1007/bf01017362
8132:Cotterman, R. L.;
7701:Departure function
7516:
7487:
7466:
7438:
7409:
7386:
7363:
7330:
7300:
7264:
7237:
7207:
7180:
7153:
7133:
7106:
7079:
7059:
7039:
7019:
6992:
6949:
6735:chemical potential
6695:
6555:
6528:
6501:
6481:
6466:
6421:
6401:
6374:
6344:
6259:
6189:
6162:
6142:
6120:
6030:
5532:
5505:
5476:
5410:
5191:
5165:
5123:
5089:
5074:
5041:
5016:
4934:
4645:
4623:
4598:
4196:
4173:
4148:
4052:
3992:
3962:
3790:
3733:
3674:
3575:
3463:chemical potential
3451:
3416:Boltzmann constant
3404:
3377:
3281:
3226:
3165:
3145:
3125:
3105:
3077:
3057:
3029:
3002:
2975:
2935:
2883:
2863:
2813:
2743:
2688:
2668:
2645:
2592:
2530:
2448:
2363:
2254:
2228:
2163:. Later, in 1802,
2138:
2062:
2033:
2004:
1979:ideal gas constant
1967:
1941:
1914:
1881:
1813:
1793:
1773:
1751:
1645:Order and disorder
1401:Reflections on the
1308:Heat death paradox
1205:
1150:
1095:
1040:
902:
878:
855:
831:
806:
770:
746:
723:
699:
674:
635:
611:
588:
564:
542:{\displaystyle c=}
539:
512:Property databases
488:Reduced properties
472:Chemical potential
436:Functions of state
359:Thermal efficiency
95:Carnot heat engine
11025:
11024:
11015:Boltzmann machine
10885:mean-field theory
10786:Maxwell relations
10663:
10662:
10645:Superheated vapor
10640:Superconductivity
10610:Equation of state
10458:Flash evaporation
10410:Phase transitions
10395:String-net liquid
10288:Photonic molecule
10258:Degenerate matter
10146:
10145:
9829:Bending of plates
9803:Johnson-Holmquist
9766:Drucker stability
9740:Contact mechanics
9687:Cauchy elasticity
9665:Equation of state
9381:978-1-4020-1954-8
8865:10.1063/1.1461829
8823:10.1063/1.1349047
8723:(10): 4168â4186.
8662:Molecular Physics
8561:10.1063/1.1674820
8547:(12): 5237â5247.
8514:10.1063/1.1701689
8500:(11): 4714â4721.
8339:10.1021/ie010954d
8333:(22): 5510â5515.
8148:(11): 1799â1812.
8136:(November 1986).
8111:10.1021/ie9600203
8105:(11): 4310â4318.
8072:10.1021/ie051305v
8066:(14): 4855â4868.
7955:Molecular Physics
7746:978-0-19-856552-9
7716:Cluster expansion
7631:
7630:
7082:{\displaystyle B}
7062:{\displaystyle A}
6947:
6885:
6813:
6683:
6661:
6614:
6511:is the pressure,
6504:{\displaystyle p}
6145:{\displaystyle e}
5474:
5448:
5408:
5380:
5312:
5180:
5138:
5105:
5056:
5031:
5006:
4978:
4917:
4875:
4855:
4804:
4777:
4750:
4626:{\displaystyle p}
4535:
4488:
4446:
4395:
4368:
4341:
4188:
4163:
4138:
4112:
3949:
3924:
3888:
3828:
3773:
3716:
3669:
3651:
3573:
3550:
3519:
3480:
3401:
3375:
3357:
3279:
3251:
3233:
3168:{\displaystyle p}
3148:{\displaystyle T}
3135:with temperature
3128:{\displaystyle V}
3108:{\displaystyle N}
3080:{\displaystyle s}
3060:{\displaystyle m}
2691:{\displaystyle b}
2671:{\displaystyle a}
2607:
2546:equation of state
2520:
2507:
2442:
2422:
2278:
2257:{\displaystyle n}
2223:
2196:
1970:{\displaystyle R}
1939:
1884:{\displaystyle n}
1816:{\displaystyle T}
1796:{\displaystyle V}
1783:is the pressure,
1776:{\displaystyle p}
1699:
1698:
1640:Self-organization
1465:
1464:
1163:Gibbs free energy
961:Maxwell relations
919:
918:
915:
914:
881:{\displaystyle V}
834:{\displaystyle 1}
789:Thermal expansion
783:
782:
749:{\displaystyle V}
702:{\displaystyle 1}
648:
647:
614:{\displaystyle N}
567:{\displaystyle T}
495:
494:
411:Process functions
397:Property diagrams
376:System properties
366:
365:
331:Endoreversibility
223:Equation of state
40:equation of state
11070:
10907:Phase transition
10728:
10727:
10690:
10683:
10676:
10667:
10666:
10600:Compressed fluid
10235:
10180:States of matter
10173:
10166:
10159:
10150:
10149:
9967:Combined gas law
9962:Gay-Lussac's law
9933:Capillary action
9798:Damage mechanics
9443:
9436:
9429:
9420:
9419:
9408:
9399:
9393:
9392:
9390:
9388:
9361:
9352:
9346:
9345:
9309:
9303:
9302:
9258:
9252:
9251:
9231:
9225:
9224:
9216:
9210:
9209:
9207:
9205:
9162:
9156:
9155:
9154:
9152:
9129:
9123:
9122:
9120:
9118:
9103:
9097:
9096:
9086:
9068:
9036:
9030:
9029:
8997:
8991:
8990:
8980:
8948:
8942:
8941:
8931:
8883:
8877:
8876:
8844:
8835:
8834:
8809:(6): 1361â1433.
8794:
8785:
8784:
8752:
8741:
8740:
8737:10.1063/1.473101
8711:
8705:
8704:
8695:(8): 1709â1721.
8684:
8678:
8677:
8657:
8648:
8647:
8639:
8628:
8627:
8579:
8573:
8572:
8532:
8526:
8525:
8485:
8479:
8478:
8454:
8448:
8447:
8407:
8401:
8400:
8391:(1â2): 174â183.
8376:
8370:
8369:
8349:
8343:
8342:
8322:
8316:
8315:
8279:
8268:
8267:
8242:(4): 1116â1126.
8227:
8221:
8220:
8188:
8182:
8181:
8134:Prausnitz, J. M.
8129:
8123:
8122:
8090:
8084:
8083:
8051:
8045:
8044:
8008:
8002:
8001:
7993:
7987:
7986:
7961:(5): 1429â1454.
7946:
7940:
7939:
7907:
7898:
7897:
7859:
7853:
7850:
7844:
7843:
7826:(6): 1197â1203.
7815:
7809:
7808:
7777:Chemical Reviews
7772:
7766:
7765:
7757:
7751:
7750:
7732:
7525:
7523:
7522:
7517:
7514:
7513:
7496:
7494:
7493:
7488:
7475:
7473:
7472:
7467:
7465:
7464:
7447:
7445:
7444:
7439:
7437:
7436:
7418:
7416:
7415:
7410:
7395:
7393:
7392:
7387:
7372:
7370:
7369:
7364:
7361:
7360:
7339:
7337:
7336:
7331:
7328:
7327:
7309:
7307:
7306:
7301:
7298:
7297:
7277:
7276:
7273:
7271:
7270:
7265:
7263:
7262:
7246:
7244:
7243:
7238:
7236:
7235:
7216:
7214:
7213:
7208:
7206:
7205:
7189:
7187:
7186:
7181:
7179:
7178:
7162:
7160:
7159:
7154:
7142:
7140:
7139:
7134:
7132:
7131:
7115:
7113:
7112:
7107:
7105:
7104:
7088:
7086:
7085:
7080:
7068:
7066:
7065:
7060:
7048:
7046:
7045:
7040:
7028:
7026:
7025:
7020:
7018:
7017:
7001:
6999:
6998:
6993:
6988:
6983:
6982:
6958:
6956:
6955:
6950:
6948:
6943:
6942:
6941:
6928:
6923:
6919:
6915:
6914:
6891:
6887:
6886:
6884:
6880:
6879:
6866:
6841:
6840:
6819:
6815:
6814:
6812:
6808:
6807:
6794:
6758:begins to form.
6704:
6702:
6701:
6696:
6694:
6693:
6688:
6684:
6682:
6681:
6669:
6662:
6660:
6646:
6633:
6632:
6616:
6612:
6602:
6601:
6564:
6562:
6561:
6556:
6554:
6553:
6537:
6535:
6534:
6529:
6527:
6526:
6510:
6508:
6507:
6502:
6490:
6488:
6487:
6482:
6479:
6474:
6465:
6464:
6430:
6428:
6427:
6422:
6410:
6408:
6407:
6402:
6400:
6399:
6383:
6381:
6380:
6375:
6373:
6372:
6353:
6351:
6350:
6345:
6343:
6342:
6333:
6332:
6317:
6316:
6268:
6266:
6265:
6260:
6255:
6250:
6246:
6245:
6244:
6218:
6217:
6198:
6196:
6195:
6190:
6188:
6187:
6171:
6169:
6168:
6163:
6151:
6149:
6148:
6143:
6129:
6127:
6126:
6121:
6118:
6117:
6065:sonoluminescence
6039:
6037:
6036:
6031:
6029:
6025:
6024:
6023:
6000:
5999:
5995:
5982:
5981:
5972:
5971:
5955:
5950:
5934:
5929:
5911:
5907:
5906:
5905:
5882:
5881:
5877:
5864:
5863:
5854:
5853:
5837:
5832:
5816:
5811:
5793:
5789:
5771:
5770:
5766:
5753:
5752:
5743:
5742:
5726:
5721:
5702:
5697:
5679:
5678:
5674:
5661:
5660:
5651:
5650:
5634:
5629:
5610:
5605:
5587:
5586:
5585:
5541:
5539:
5538:
5533:
5531:
5530:
5514:
5512:
5511:
5506:
5504:
5503:
5485:
5483:
5482:
5477:
5475:
5473:
5472:
5460:
5449:
5444:
5443:
5434:
5419:
5417:
5416:
5411:
5409:
5407:
5399:
5383:
5382:
5381:
5378:
5353:
5352:
5351:
5318:
5313:
5311:
5303:
5283:
5255:hydrogen bonding
5251:Helmholtz energy
5200:
5198:
5197:
5192:
5190:
5186:
5185:
5181:
5178:
5173:
5164:
5156:
5144:
5140:
5139:
5136:
5131:
5119:
5106:
5104:
5102:
5097:
5087:
5082:
5072:
5071:
5062:
5057:
5054:
5049:
5037:
5032:
5029:
5024:
5012:
5007:
5005:
5004:
4992:
4979:
4974:
4966:
4943:
4941:
4940:
4935:
4933:
4932:
4923:
4919:
4918:
4910:
4891:
4890:
4881:
4877:
4876:
4874:
4873:
4861:
4856:
4848:
4820:
4819:
4810:
4806:
4805:
4803:
4802:
4793:
4792:
4783:
4778:
4776:
4775:
4766:
4765:
4756:
4751:
4749:
4748:
4739:
4738:
4729:
4724:
4723:
4705:
4704:
4655:is molar density
4654:
4652:
4651:
4646:
4632:
4630:
4629:
4624:
4607:
4605:
4604:
4599:
4597:
4593:
4592:
4591:
4565:
4561:
4560:
4559:
4536:
4534:
4533:
4524:
4523:
4522:
4509:
4504:
4503:
4494:
4490:
4489:
4481:
4462:
4461:
4452:
4448:
4447:
4439:
4411:
4410:
4401:
4397:
4396:
4394:
4393:
4384:
4383:
4374:
4369:
4367:
4366:
4357:
4356:
4347:
4342:
4340:
4339:
4330:
4329:
4320:
4315:
4314:
4296:
4295:
4214:Kamerlingh Onnes
4205:
4203:
4202:
4197:
4189:
4186:
4181:
4169:
4164:
4161:
4156:
4144:
4139:
4137:
4136:
4124:
4113:
4111:
4103:
4102:
4101:
4088:
4077:Virial expansion
4061:
4059:
4058:
4053:
4051:
4050:
4001:
3999:
3998:
3993:
3988:
3971:
3969:
3968:
3963:
3961:
3957:
3950:
3948:
3947:
3946:
3942:
3926:
3925:
3922:
3906:
3905:
3904:
3891:
3889:
3887:
3864:
3863:
3859:
3846:
3830:
3829:
3826:
3799:
3797:
3796:
3791:
3783:
3782:
3775:
3774:
3771:
3762:
3742:
3740:
3739:
3734:
3726:
3725:
3718:
3717:
3714:
3705:
3683:
3681:
3680:
3675:
3670:
3668:
3661:
3660:
3653:
3652:
3649:
3640:
3620:
3616:
3610:
3609:
3605:
3591:
3588:
3583:
3574:
3572:
3571:
3570:
3561:
3560:
3551:
3546:
3543:
3542:
3541:
3537:
3521:
3520:
3517:
3486:
3481:
3473:
3460:
3458:
3457:
3452:
3444:
3413:
3411:
3410:
3405:
3403:
3402:
3399:
3386:
3384:
3383:
3378:
3376:
3374:
3367:
3366:
3359:
3358:
3355:
3346:
3326:
3322:
3316:
3315:
3311:
3297:
3294:
3289:
3280:
3278:
3277:
3276:
3267:
3266:
3253:
3252:
3250:
3249:
3239:
3234:
3231:
3225:
3224:
3212:
3191:
3174:
3172:
3171:
3166:
3154:
3152:
3151:
3146:
3134:
3132:
3131:
3126:
3114:
3112:
3111:
3106:
3086:
3084:
3083:
3078:
3066:
3064:
3063:
3058:
3038:
3036:
3035:
3030:
3028:
3027:
3011:
3009:
3008:
3003:
3001:
3000:
2984:
2982:
2981:
2976:
2971:
2970:
2944:
2942:
2941:
2936:
2934:
2933:
2924:
2919:
2918:
2892:
2890:
2889:
2884:
2872:
2870:
2869:
2864:
2822:
2820:
2819:
2814:
2752:
2750:
2749:
2744:
2697:
2695:
2694:
2689:
2677:
2675:
2674:
2669:
2654:
2652:
2651:
2646:
2626:
2625:
2613:
2609:
2608:
2605:
2600:
2588:
2539:
2537:
2536:
2531:
2526:
2522:
2521:
2518:
2516:
2515:
2510:
2505:
2498:
2497:
2477:
2476:
2457:
2455:
2454:
2449:
2447:
2440:
2433:
2428:
2427:
2420:
2372:
2370:
2369:
2364:
2359:
2358:
2348:
2343:
2325:
2324:
2306:
2305:
2293:
2292:
2280:
2279:
2276:
2263:
2261:
2260:
2255:
2237:
2235:
2234:
2229:
2224:
2222:
2221:
2212:
2211:
2202:
2197:
2195:
2194:
2185:
2184:
2175:
2147:
2145:
2144:
2139:
2134:
2071:
2069:
2068:
2063:
2061:
2060:
2042:
2040:
2039:
2034:
2032:
2031:
2013:
2011:
2010:
2005:
2003:
2002:
1984:
1976:
1974:
1973:
1968:
1950:
1948:
1947:
1942:
1940:
1932:
1923:
1921:
1920:
1915:
1913:
1912:
1890:
1888:
1887:
1882:
1835:, dense matter (
1825:Gibbs phase rule
1822:
1820:
1819:
1814:
1803:the volume, and
1802:
1800:
1799:
1794:
1782:
1780:
1779:
1774:
1760:
1758:
1757:
1752:
1691:
1684:
1677:
1661:
1660:
1368:Key publications
1349:
1348:("living force")
1298:Brownian ratchet
1293:Entropy and life
1288:Entropy and time
1239:
1238:
1214:
1212:
1211:
1206:
1159:
1157:
1156:
1151:
1104:
1102:
1101:
1096:
1049:
1047:
1046:
1041:
943:Clausius theorem
938:Carnot's theorem
911:
909:
908:
903:
887:
885:
884:
879:
864:
862:
861:
856:
840:
838:
837:
832:
819:
818:
815:
813:
812:
807:
779:
777:
776:
771:
755:
753:
752:
747:
732:
730:
729:
724:
708:
706:
705:
700:
687:
686:
683:
681:
680:
675:
644:
642:
641:
636:
620:
618:
617:
612:
597:
595:
594:
589:
573:
571:
570:
565:
552:
551:
548:
546:
545:
540:
518:
517:
391:
390:
210:
209:
91:
77:
76:
11078:
11077:
11073:
11072:
11071:
11069:
11068:
11067:
11053:Fluid mechanics
11028:
11027:
11026:
11021:
10966:
10928:
10893:
10875:BBGKY hierarchy
10870:Vlasov equation
10848:
10837:depletion force
10830:Particles with
10790:
10729:
10725:
10720:
10699:
10694:
10664:
10659:
10590:Baryonic matter
10578:
10532:
10503:Saturated fluid
10443:Crystallization
10404:
10378:Antiferromagnet
10318:
10292:
10236:
10227:
10187:
10177:
10147:
10142:
10119:
10051:
10015:Viscoelasticity
10001:
9992:Acoustic theory
9978:
9928:Surface tension
9846:Fluid mechanics
9840:
9834:Sandwich theory
9726:Yield criterion
9721:Viscoplasticity
9692:Viscoelasticity
9653:hyperelasticity
9603:
9587:Antiplane shear
9570:Stress measures
9489:
9470:Fluid mechanics
9465:Solid mechanics
9453:
9447:
9417:
9412:
9411:
9400:
9396:
9386:
9384:
9382:
9359:
9353:
9349:
9314:High Press. Res
9310:
9306:
9263:Rep. Prog. Phys
9259:
9255:
9236:High Press. Res
9232:
9228:
9217:
9213:
9203:
9201:
9163:
9159:
9150:
9148:
9146:
9130:
9126:
9116:
9114:
9104:
9100:
9037:
9033:
8998:
8994:
8949:
8945:
8884:
8880:
8845:
8838:
8795:
8788:
8753:
8744:
8712:
8708:
8685:
8681:
8658:
8651:
8640:
8631:
8580:
8576:
8533:
8529:
8486:
8482:
8455:
8451:
8416:Physical Review
8408:
8404:
8377:
8373:
8350:
8346:
8323:
8319:
8280:
8271:
8228:
8224:
8189:
8185:
8130:
8126:
8091:
8087:
8052:
8048:
8009:
8005:
7994:
7990:
7947:
7943:
7908:
7901:
7878:
7860:
7856:
7851:
7847:
7816:
7812:
7773:
7769:
7758:
7754:
7747:
7733:
7729:
7724:
7692:
7636:
7509:
7505:
7503:
7500:
7499:
7482:
7479:
7478:
7460:
7456:
7454:
7451:
7450:
7432:
7428:
7426:
7423:
7422:
7403:
7400:
7399:
7380:
7377:
7376:
7353:
7349:
7347:
7344:
7343:
7323:
7319:
7317:
7314:
7313:
7293:
7289:
7287:
7284:
7283:
7258:
7254:
7252:
7249:
7248:
7228:
7224:
7222:
7219:
7218:
7201:
7197:
7195:
7192:
7191:
7174:
7170:
7168:
7165:
7164:
7148:
7145:
7144:
7127:
7123:
7121:
7118:
7117:
7100:
7096:
7094:
7091:
7090:
7074:
7071:
7070:
7054:
7051:
7050:
7034:
7031:
7030:
7013:
7009:
7007:
7004:
7003:
6984:
6978:
6974:
6966:
6963:
6962:
6937:
6933:
6929:
6927:
6910:
6906:
6902:
6898:
6875:
6871:
6870:
6865:
6858:
6854:
6836:
6832:
6803:
6799:
6798:
6793:
6786:
6782:
6771:
6768:
6767:
6764:
6753:
6725:
6689:
6677:
6673:
6668:
6664:
6663:
6647:
6622:
6618:
6617:
6615:
6597:
6593:
6588:
6585:
6584:
6575:
6549:
6545:
6543:
6540:
6539:
6522:
6518:
6516:
6513:
6512:
6496:
6493:
6492:
6475:
6470:
6460:
6456:
6448:
6445:
6444:
6437:
6416:
6413:
6412:
6395:
6391:
6389:
6386:
6385:
6368:
6364:
6362:
6359:
6358:
6356:
6338:
6334:
6328:
6324:
6312:
6308:
6300:
6297:
6296:
6295:
6290:
6251:
6240:
6236:
6229:
6225:
6213:
6209:
6207:
6204:
6203:
6183:
6179:
6177:
6174:
6173:
6157:
6154:
6153:
6137:
6134:
6133:
6113:
6109:
6074:
6071:
6070:
6053:
6048:
6019:
6015:
6011:
6007:
5991:
5987:
5983:
5977:
5973:
5961:
5957:
5951:
5940:
5930:
5919:
5901:
5897:
5893:
5889:
5873:
5869:
5865:
5859:
5855:
5843:
5839:
5833:
5822:
5812:
5801:
5782:
5778:
5762:
5758:
5754:
5748:
5744:
5732:
5728:
5722:
5708:
5698:
5687:
5670:
5666:
5662:
5656:
5652:
5640:
5636:
5630:
5616:
5606:
5595:
5560:
5559:
5555:
5553:
5550:
5549:
5526:
5522:
5520:
5517:
5516:
5499:
5495:
5493:
5490:
5489:
5468:
5464:
5459:
5439:
5435:
5433:
5425:
5422:
5421:
5400:
5377:
5376:
5372:
5325:
5324:
5320:
5319:
5317:
5304:
5284:
5282:
5280:
5277:
5276:
5272:
5243:
5231:
5206:
5174:
5169:
5157:
5155:
5151:
5132:
5127:
5118:
5111:
5107:
5098:
5093:
5083:
5078:
5073:
5067:
5063:
5061:
5050:
5045:
5036:
5025:
5020:
5011:
5000:
4996:
4991:
4984:
4980:
4967:
4965:
4957:
4954:
4953:
4928:
4924:
4909:
4902:
4898:
4886:
4882:
4869:
4865:
4860:
4847:
4828:
4824:
4815:
4811:
4798:
4794:
4788:
4784:
4782:
4771:
4767:
4761:
4757:
4755:
4744:
4740:
4734:
4730:
4728:
4719:
4715:
4700:
4696:
4695:
4691:
4671:
4668:
4667:
4640:
4637:
4636:
4618:
4615:
4614:
4587:
4583:
4576:
4572:
4555:
4551:
4541:
4537:
4529:
4525:
4518:
4514:
4510:
4508:
4499:
4495:
4480:
4473:
4469:
4457:
4453:
4438:
4419:
4415:
4406:
4402:
4389:
4385:
4379:
4375:
4373:
4362:
4358:
4352:
4348:
4346:
4335:
4331:
4325:
4321:
4319:
4310:
4306:
4291:
4287:
4286:
4282:
4262:
4259:
4258:
4256:
4250:
4182:
4177:
4168:
4157:
4152:
4143:
4132:
4128:
4123:
4104:
4097:
4093:
4089:
4087:
4085:
4082:
4081:
4079:
4073:
4068:
4046:
4042:
4040:
4037:
4036:
4026:
4020:
3984:
3979:
3976:
3975:
3938:
3934:
3930:
3921:
3917:
3907:
3900:
3896:
3892:
3890:
3865:
3855:
3851:
3847:
3845:
3838:
3834:
3825:
3821:
3807:
3804:
3803:
3770:
3766:
3758:
3754:
3750:
3748:
3745:
3744:
3713:
3709:
3701:
3697:
3693:
3691:
3688:
3687:
3648:
3644:
3636:
3626:
3622:
3621:
3612:
3601:
3597:
3593:
3592:
3590:
3584:
3579:
3566:
3562:
3556:
3552:
3545:
3544:
3533:
3529:
3525:
3516:
3512:
3487:
3485:
3472:
3470:
3467:
3466:
3440:
3423:
3420:
3419:
3398:
3394:
3392:
3389:
3388:
3354:
3350:
3342:
3332:
3328:
3327:
3318:
3307:
3303:
3299:
3298:
3296:
3290:
3285:
3272:
3268:
3262:
3258:
3254:
3245:
3241:
3235:
3230:
3220:
3216:
3211:
3192:
3190:
3182:
3179:
3178:
3160:
3157:
3156:
3140:
3137:
3136:
3120:
3117:
3116:
3100:
3097:
3096:
3072:
3069:
3068:
3052:
3049:
3048:
3045:
3023:
3019:
3017:
3014:
3013:
2996:
2992:
2990:
2987:
2986:
2966:
2962:
2954:
2951:
2950:
2929:
2925:
2920:
2914:
2910:
2902:
2899:
2898:
2878:
2875:
2874:
2834:
2831:
2830:
2760:
2757:
2756:
2720:
2717:
2716:
2715:may be written
2709:
2704:
2683:
2680:
2679:
2663:
2660:
2659:
2621:
2617:
2601:
2596:
2587:
2577:
2573:
2571:
2568:
2567:
2517:
2511:
2509:
2508:
2493:
2489:
2488:
2484:
2472:
2468:
2463:
2460:
2459:
2443:
2429:
2423:
2419:
2414:
2411:
2410:
2399:
2388:
2375:Ămile Clapeyron
2354:
2350:
2344:
2333:
2320:
2316:
2301:
2297:
2288:
2284:
2275:
2271:
2269:
2266:
2265:
2249:
2246:
2245:
2217:
2213:
2207:
2203:
2201:
2190:
2186:
2180:
2176:
2174:
2172:
2169:
2168:
2157:Jacques Charles
2109:
2098:
2095:
2094:
2079:
2056:
2052:
2050:
2047:
2046:
2027:
2023:
2021:
2018:
2017:
1998:
1994:
1992:
1989:
1988:
1982:
1962:
1959:
1958:
1931:
1929:
1926:
1925:
1908:
1904:
1902:
1899:
1898:
1876:
1873:
1872:
1808:
1805:
1804:
1788:
1785:
1784:
1768:
1765:
1764:
1719:
1716:
1715:
1704:
1695:
1650:
1649:
1625:
1617:
1616:
1615:
1475:
1467:
1466:
1445:
1431:
1406:
1402:
1395:
1391:
1384:
1380:
1347:
1340:
1322:
1303:Maxwell's demon
1265:
1236:
1235:
1219:
1218:
1217:
1170:
1167:
1166:
1165:
1115:
1112:
1111:
1110:
1060:
1057:
1056:
1055:
1020:
1017:
1016:
1015:
1013:Internal energy
1008:
993:
983:
982:
957:
932:
922:
921:
920:
894:
891:
890:
873:
870:
869:
847:
844:
843:
826:
823:
822:
798:
795:
794:
762:
759:
758:
741:
738:
737:
715:
712:
711:
694:
691:
690:
663:
660:
659:
654:Compressibility
627:
624:
623:
606:
603:
602:
580:
577:
576:
559:
556:
555:
531:
528:
527:
507:
497:
496:
477:Particle number
430:
389:
378:
368:
367:
326:Irreversibility
238:State of matter
205:Isolated system
190:
180:
179:
178:
153:
143:
142:
138:Non-equilibrium
130:
105:
97:
64:internal energy
48:state variables
28:
17:
12:
11:
5:
11076:
11066:
11065:
11060:
11055:
11050:
11045:
11040:
11023:
11022:
11020:
11019:
11018:
11017:
11012:
11007:
11000:Complex system
10997:
10992:
10991:
10990:
10985:
10974:
10972:
10968:
10967:
10965:
10964:
10959:
10954:
10949:
10944:
10938:
10936:
10930:
10929:
10927:
10926:
10925:
10924:
10919:
10909:
10903:
10901:
10895:
10894:
10892:
10891:
10882:
10877:
10872:
10867:
10862:
10856:
10854:
10850:
10849:
10847:
10846:
10845:
10844:
10839:
10828:
10827:
10826:
10821:
10816:
10811:
10800:
10798:
10792:
10791:
10789:
10788:
10783:
10782:
10781:
10776:
10771:
10766:
10755:
10750:
10745:
10739:
10737:
10731:
10730:
10723:
10721:
10719:
10718:
10716:ergodic theory
10713:
10707:
10705:
10701:
10700:
10693:
10692:
10685:
10678:
10670:
10661:
10660:
10658:
10657:
10652:
10647:
10642:
10637:
10632:
10627:
10622:
10617:
10612:
10607:
10602:
10597:
10592:
10586:
10584:
10580:
10579:
10577:
10576:
10571:
10569:Trouton's rule
10566:
10561:
10556:
10551:
10546:
10540:
10538:
10534:
10533:
10531:
10530:
10525:
10520:
10515:
10510:
10505:
10500:
10495:
10490:
10485:
10480:
10475:
10470:
10465:
10460:
10455:
10450:
10445:
10440:
10438:Critical point
10435:
10430:
10425:
10420:
10414:
10412:
10406:
10405:
10403:
10402:
10397:
10392:
10391:
10390:
10385:
10380:
10372:
10367:
10362:
10357:
10352:
10347:
10342:
10340:Liquid crystal
10337:
10332:
10326:
10324:
10320:
10319:
10317:
10316:
10311:
10306:
10300:
10298:
10294:
10293:
10291:
10290:
10285:
10280:
10275:
10273:Strange matter
10270:
10268:Rydberg matter
10265:
10260:
10255:
10250:
10244:
10242:
10238:
10237:
10230:
10228:
10226:
10225:
10220:
10215:
10206:
10201:
10195:
10193:
10189:
10188:
10176:
10175:
10168:
10161:
10153:
10144:
10143:
10141:
10140:
10135:
10129:
10127:
10121:
10120:
10118:
10117:
10112:
10107:
10102:
10097:
10092:
10087:
10082:
10077:
10072:
10067:
10061:
10059:
10053:
10052:
10050:
10049:
10044:
10039:
10038:
10037:
10032:
10027:
10017:
10011:
10009:
10003:
10002:
10000:
9999:
9994:
9988:
9986:
9980:
9979:
9977:
9976:
9970:
9969:
9964:
9959:
9954:
9949:
9943:
9942:
9936:
9935:
9930:
9925:
9920:
9915:
9910:
9905:
9904:
9903:
9898:
9888:
9883:
9878:
9873:
9868:
9866:Fluid dynamics
9863:
9857:
9856:
9850:
9848:
9842:
9841:
9839:
9838:
9837:
9836:
9831:
9826:
9824:Bending moment
9815:
9814:
9808:
9807:
9806:
9805:
9795:
9794:
9793:
9788:
9778:
9773:
9768:
9762:
9761:
9755:
9754:
9753:
9752:
9747:
9737:
9736:
9735:
9734:
9733:
9731:Bresler-Pister
9723:
9718:
9708:
9707:
9706:
9705:
9704:
9702:Concrete creep
9699:
9689:
9684:
9682:hypoelasticity
9679:
9678:
9677:
9672:
9662:
9661:
9660:
9650:
9645:
9640:
9635:
9624:
9623:
9617:
9615:
9605:
9604:
9602:
9601:
9596:
9591:
9590:
9589:
9579:
9574:
9573:
9572:
9567:
9556:
9555:
9551:
9550:
9545:
9540:
9539:
9538:
9533:
9528:
9523:
9518:
9508:
9502:
9501:
9497:
9495:
9491:
9490:
9488:
9487:
9482:
9477:
9472:
9467:
9461:
9459:
9455:
9454:
9446:
9445:
9438:
9431:
9423:
9416:
9415:External links
9413:
9410:
9409:
9394:
9380:
9347:
9304:
9253:
9226:
9211:
9177:(3): 189â232.
9157:
9144:
9124:
9098:
9031:
9012:(3): 265â276.
8992:
8943:
8878:
8859:(2): 387â535.
8836:
8786:
8742:
8706:
8679:
8649:
8629:
8594:(1â2): 19â34.
8574:
8527:
8480:
8449:
8422:(1): 307â316.
8402:
8371:
8344:
8317:
8269:
8222:
8203:(3): 705â717.
8183:
8124:
8085:
8046:
8019:(3): 510â527.
8003:
7988:
7941:
7899:
7876:
7854:
7845:
7810:
7783:(1): 233â244.
7767:
7752:
7745:
7726:
7725:
7723:
7720:
7719:
7718:
7713:
7708:
7703:
7698:
7691:
7688:
7687:
7686:
7681:
7676:
7671:
7666:
7663:
7660:
7657:
7652:
7647:
7635:
7632:
7629:
7628:
7625:
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7610:
7607:
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7508:
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7407:
7397:
7384:
7374:
7359:
7356:
7352:
7341:
7326:
7322:
7311:
7296:
7292:
7281:
7261:
7257:
7234:
7231:
7227:
7204:
7200:
7177:
7173:
7152:
7130:
7126:
7103:
7099:
7078:
7058:
7038:
7016:
7012:
6991:
6987:
6981:
6977:
6973:
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6946:
6940:
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6926:
6922:
6918:
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6909:
6905:
6901:
6897:
6894:
6890:
6883:
6878:
6874:
6869:
6864:
6861:
6857:
6853:
6850:
6847:
6844:
6839:
6835:
6831:
6828:
6825:
6822:
6818:
6811:
6806:
6802:
6797:
6792:
6789:
6785:
6781:
6778:
6775:
6763:
6760:
6749:
6723:
6692:
6687:
6680:
6676:
6672:
6667:
6659:
6656:
6653:
6650:
6645:
6642:
6639:
6636:
6631:
6628:
6625:
6621:
6611:
6608:
6605:
6600:
6596:
6592:
6574:
6571:
6567:speed of sound
6552:
6548:
6525:
6521:
6500:
6478:
6473:
6469:
6463:
6459:
6455:
6452:
6436:
6433:
6420:
6398:
6394:
6371:
6367:
6341:
6337:
6331:
6327:
6323:
6320:
6315:
6311:
6307:
6304:
6289:
6286:
6258:
6254:
6249:
6243:
6239:
6235:
6232:
6228:
6224:
6221:
6216:
6212:
6186:
6182:
6161:
6141:
6116:
6112:
6108:
6105:
6102:
6099:
6096:
6093:
6090:
6087:
6084:
6081:
6078:
6052:
6049:
6047:
6044:
6028:
6022:
6018:
6014:
6010:
6006:
6003:
5998:
5994:
5990:
5986:
5980:
5976:
5970:
5967:
5964:
5960:
5954:
5949:
5946:
5943:
5939:
5933:
5928:
5925:
5922:
5918:
5914:
5910:
5904:
5900:
5896:
5892:
5888:
5885:
5880:
5876:
5872:
5868:
5862:
5858:
5852:
5849:
5846:
5842:
5836:
5831:
5828:
5825:
5821:
5815:
5810:
5807:
5804:
5800:
5796:
5792:
5788:
5785:
5781:
5777:
5774:
5769:
5765:
5761:
5757:
5751:
5747:
5741:
5738:
5735:
5731:
5725:
5720:
5717:
5714:
5711:
5707:
5701:
5696:
5693:
5690:
5686:
5682:
5677:
5673:
5669:
5665:
5659:
5655:
5649:
5646:
5643:
5639:
5633:
5628:
5625:
5622:
5619:
5615:
5609:
5604:
5601:
5598:
5594:
5590:
5584:
5581:
5578:
5575:
5572:
5569:
5566:
5563:
5558:
5529:
5525:
5502:
5498:
5471:
5467:
5463:
5458:
5455:
5452:
5447:
5442:
5438:
5432:
5429:
5406:
5403:
5398:
5395:
5392:
5389:
5386:
5375:
5371:
5368:
5365:
5362:
5359:
5356:
5350:
5347:
5344:
5340:
5337:
5334:
5331:
5328:
5323:
5316:
5310:
5307:
5302:
5299:
5296:
5293:
5290:
5287:
5271:
5268:
5242:
5239:
5230:
5227:
5205:
5202:
5189:
5184:
5177:
5172:
5168:
5163:
5160:
5154:
5150:
5147:
5143:
5135:
5130:
5126:
5122:
5117:
5114:
5110:
5101:
5096:
5092:
5086:
5081:
5077:
5070:
5066:
5060:
5053:
5048:
5044:
5040:
5035:
5028:
5023:
5019:
5015:
5010:
5003:
4999:
4995:
4990:
4987:
4983:
4977:
4973:
4970:
4964:
4961:
4931:
4927:
4922:
4916:
4913:
4908:
4905:
4901:
4897:
4894:
4889:
4885:
4880:
4872:
4868:
4864:
4859:
4854:
4851:
4846:
4843:
4840:
4837:
4834:
4831:
4827:
4823:
4818:
4814:
4809:
4801:
4797:
4791:
4787:
4781:
4774:
4770:
4764:
4760:
4754:
4747:
4743:
4737:
4733:
4727:
4722:
4718:
4714:
4711:
4708:
4703:
4699:
4694:
4690:
4687:
4684:
4681:
4678:
4675:
4657:
4656:
4644:
4634:
4622:
4596:
4590:
4586:
4582:
4579:
4575:
4571:
4568:
4564:
4558:
4554:
4550:
4547:
4544:
4540:
4532:
4528:
4521:
4517:
4513:
4507:
4502:
4498:
4493:
4487:
4484:
4479:
4476:
4472:
4468:
4465:
4460:
4456:
4451:
4445:
4442:
4437:
4434:
4431:
4428:
4425:
4422:
4418:
4414:
4409:
4405:
4400:
4392:
4388:
4382:
4378:
4372:
4365:
4361:
4355:
4351:
4345:
4338:
4334:
4328:
4324:
4318:
4313:
4309:
4305:
4302:
4299:
4294:
4290:
4285:
4281:
4278:
4275:
4272:
4269:
4266:
4252:Main article:
4249:
4246:
4195:
4192:
4185:
4180:
4176:
4172:
4167:
4160:
4155:
4151:
4147:
4142:
4135:
4131:
4127:
4122:
4119:
4116:
4110:
4107:
4100:
4096:
4092:
4075:Main article:
4072:
4069:
4067:
4064:
4049:
4045:
4033:cubic function
4022:Main article:
4019:
4016:
3991:
3987:
3983:
3960:
3956:
3953:
3945:
3941:
3937:
3933:
3929:
3920:
3916:
3913:
3910:
3903:
3899:
3895:
3886:
3883:
3880:
3877:
3874:
3871:
3868:
3862:
3858:
3854:
3850:
3844:
3841:
3837:
3833:
3824:
3820:
3817:
3814:
3811:
3789:
3786:
3781:
3778:
3769:
3765:
3761:
3757:
3753:
3732:
3729:
3724:
3721:
3712:
3708:
3704:
3700:
3696:
3673:
3667:
3664:
3659:
3656:
3647:
3643:
3639:
3635:
3632:
3629:
3625:
3619:
3615:
3608:
3604:
3600:
3596:
3587:
3582:
3578:
3569:
3565:
3559:
3555:
3549:
3540:
3536:
3532:
3528:
3524:
3515:
3511:
3508:
3505:
3502:
3499:
3496:
3493:
3490:
3484:
3479:
3476:
3450:
3447:
3443:
3439:
3436:
3433:
3430:
3427:
3397:
3373:
3370:
3365:
3362:
3353:
3349:
3345:
3341:
3338:
3335:
3331:
3325:
3321:
3314:
3310:
3306:
3302:
3293:
3288:
3284:
3275:
3271:
3265:
3261:
3257:
3248:
3244:
3238:
3229:
3223:
3219:
3215:
3210:
3207:
3204:
3201:
3198:
3195:
3189:
3186:
3164:
3144:
3124:
3104:
3076:
3056:
3044:
3041:
3026:
3022:
2999:
2995:
2974:
2969:
2965:
2961:
2958:
2932:
2928:
2923:
2917:
2913:
2909:
2906:
2895:number density
2882:
2862:
2859:
2856:
2853:
2850:
2847:
2844:
2841:
2838:
2812:
2809:
2806:
2803:
2800:
2797:
2794:
2791:
2788:
2785:
2782:
2779:
2776:
2773:
2770:
2767:
2764:
2742:
2739:
2736:
2733:
2730:
2727:
2724:
2711:The classical
2708:
2705:
2703:
2700:
2687:
2667:
2656:
2655:
2644:
2641:
2638:
2635:
2632:
2629:
2624:
2620:
2616:
2612:
2604:
2599:
2595:
2591:
2586:
2583:
2580:
2576:
2529:
2525:
2514:
2504:
2501:
2496:
2492:
2487:
2483:
2480:
2475:
2471:
2467:
2446:
2439:
2436:
2432:
2426:
2418:
2397:
2386:
2362:
2357:
2353:
2347:
2342:
2339:
2336:
2332:
2328:
2323:
2319:
2315:
2312:
2309:
2304:
2300:
2296:
2291:
2287:
2283:
2274:
2253:
2227:
2220:
2216:
2210:
2206:
2200:
2193:
2189:
2183:
2179:
2137:
2133:
2130:
2127:
2124:
2121:
2118:
2115:
2112:
2108:
2105:
2102:
2078:
2075:
2074:
2073:
2059:
2055:
2044:
2030:
2026:
2015:
2001:
1997:
1986:
1966:
1956:
1938:
1935:
1911:
1907:
1896:
1895:of a substance
1880:
1812:
1792:
1772:
1750:
1747:
1744:
1741:
1738:
1735:
1732:
1729:
1726:
1723:
1703:
1700:
1697:
1696:
1694:
1693:
1686:
1679:
1671:
1668:
1667:
1666:
1665:
1652:
1651:
1648:
1647:
1642:
1637:
1632:
1626:
1623:
1622:
1619:
1618:
1614:
1613:
1608:
1603:
1598:
1593:
1588:
1583:
1578:
1573:
1568:
1563:
1558:
1553:
1548:
1543:
1538:
1533:
1528:
1523:
1518:
1513:
1508:
1503:
1498:
1493:
1488:
1483:
1477:
1476:
1473:
1472:
1469:
1468:
1463:
1462:
1461:
1460:
1455:
1447:
1446:
1444:
1443:
1440:
1436:
1433:
1432:
1430:
1429:
1424:
1422:Thermodynamics
1418:
1415:
1414:
1410:
1409:
1408:
1407:
1398:
1396:
1387:
1385:
1376:
1371:
1370:
1364:
1363:
1362:
1361:
1356:
1351:
1339:
1338:
1336:Caloric theory
1332:
1329:
1328:
1324:
1323:
1321:
1320:
1315:
1310:
1305:
1300:
1295:
1290:
1284:
1281:
1280:
1274:
1273:
1272:
1271:
1264:
1263:
1258:
1253:
1247:
1244:
1243:
1237:
1234:
1233:
1230:
1226:
1225:
1224:
1221:
1220:
1216:
1215:
1204:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1160:
1149:
1146:
1143:
1140:
1137:
1134:
1131:
1128:
1125:
1122:
1119:
1105:
1094:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1050:
1039:
1036:
1033:
1030:
1027:
1024:
1009:
1007:
1006:
1001:
995:
994:
989:
988:
985:
984:
981:
980:
973:
968:
963:
956:
955:
950:
945:
940:
934:
933:
928:
927:
924:
923:
917:
916:
913:
912:
901:
898:
888:
877:
866:
865:
854:
851:
841:
830:
816:
805:
802:
792:
785:
784:
781:
780:
769:
766:
756:
745:
734:
733:
722:
719:
709:
698:
684:
673:
670:
667:
657:
650:
649:
646:
645:
634:
631:
621:
610:
599:
598:
587:
584:
574:
563:
549:
538:
535:
525:
516:
515:
514:
508:
503:
502:
499:
498:
493:
492:
491:
490:
485:
480:
469:
458:
439:
438:
432:
431:
429:
428:
423:
417:
414:
413:
407:
406:
405:
404:
399:
380:
379:
374:
373:
370:
369:
364:
363:
362:
361:
356:
351:
343:
342:
336:
335:
334:
333:
328:
323:
318:
316:Free expansion
313:
308:
303:
298:
293:
288:
283:
278:
270:
269:
263:
262:
261:
260:
255:
253:Control volume
250:
245:
243:Phase (matter)
240:
235:
230:
225:
217:
216:
208:
207:
202:
197:
191:
186:
185:
182:
181:
177:
176:
171:
166:
161:
155:
154:
149:
148:
145:
144:
141:
140:
129:
128:
123:
118:
113:
107:
106:
103:
102:
99:
98:
93:The classical
92:
84:
83:
81:Thermodynamics
15:
9:
6:
4:
3:
2:
11075:
11064:
11061:
11059:
11056:
11054:
11051:
11049:
11046:
11044:
11041:
11039:
11036:
11035:
11033:
11016:
11013:
11011:
11008:
11006:
11003:
11002:
11001:
10998:
10996:
10993:
10989:
10988:superfluidity
10986:
10984:
10981:
10980:
10979:
10976:
10975:
10973:
10969:
10963:
10960:
10958:
10955:
10953:
10950:
10948:
10945:
10943:
10940:
10939:
10937:
10935:
10931:
10923:
10920:
10918:
10915:
10914:
10913:
10910:
10908:
10905:
10904:
10902:
10900:
10896:
10890:
10886:
10883:
10881:
10878:
10876:
10873:
10871:
10868:
10866:
10863:
10861:
10858:
10857:
10855:
10851:
10843:
10840:
10838:
10835:
10834:
10833:
10829:
10825:
10822:
10820:
10817:
10815:
10812:
10810:
10807:
10806:
10805:
10802:
10801:
10799:
10797:
10793:
10787:
10784:
10780:
10777:
10775:
10772:
10770:
10767:
10765:
10762:
10761:
10759:
10756:
10754:
10751:
10749:
10746:
10744:
10741:
10740:
10738:
10736:
10732:
10717:
10714:
10712:
10709:
10708:
10706:
10702:
10698:
10691:
10686:
10684:
10679:
10677:
10672:
10671:
10668:
10656:
10653:
10651:
10648:
10646:
10643:
10641:
10638:
10636:
10633:
10631:
10628:
10626:
10625:Mpemba effect
10623:
10621:
10618:
10616:
10613:
10611:
10608:
10606:
10605:Cooling curve
10603:
10601:
10598:
10596:
10593:
10591:
10588:
10587:
10585:
10581:
10575:
10572:
10570:
10567:
10565:
10562:
10560:
10557:
10555:
10552:
10550:
10547:
10545:
10542:
10541:
10539:
10535:
10529:
10528:Vitrification
10526:
10524:
10521:
10519:
10516:
10514:
10511:
10509:
10506:
10504:
10501:
10499:
10496:
10494:
10493:Recombination
10491:
10489:
10488:Melting point
10486:
10484:
10481:
10479:
10476:
10474:
10471:
10469:
10466:
10464:
10461:
10459:
10456:
10454:
10451:
10449:
10446:
10444:
10441:
10439:
10436:
10434:
10433:Critical line
10431:
10429:
10426:
10424:
10423:Boiling point
10421:
10419:
10416:
10415:
10413:
10411:
10407:
10401:
10398:
10396:
10393:
10389:
10386:
10384:
10381:
10379:
10376:
10375:
10373:
10371:
10368:
10366:
10363:
10361:
10358:
10356:
10355:Exotic matter
10353:
10351:
10348:
10346:
10343:
10341:
10338:
10336:
10333:
10331:
10328:
10327:
10325:
10321:
10315:
10312:
10310:
10307:
10305:
10302:
10301:
10299:
10295:
10289:
10286:
10284:
10281:
10279:
10276:
10274:
10271:
10269:
10266:
10264:
10261:
10259:
10256:
10254:
10251:
10249:
10246:
10245:
10243:
10239:
10234:
10224:
10221:
10219:
10216:
10214:
10210:
10207:
10205:
10202:
10200:
10197:
10196:
10194:
10190:
10185:
10181:
10174:
10169:
10167:
10162:
10160:
10155:
10154:
10151:
10139:
10136:
10134:
10133:Eringen Medal
10131:
10130:
10128:
10126:
10122:
10116:
10113:
10111:
10108:
10106:
10103:
10101:
10098:
10096:
10093:
10091:
10088:
10086:
10083:
10081:
10078:
10076:
10073:
10071:
10068:
10066:
10063:
10062:
10060:
10058:
10054:
10048:
10045:
10043:
10040:
10036:
10033:
10031:
10028:
10026:
10023:
10022:
10021:
10018:
10016:
10013:
10012:
10010:
10008:
10004:
9998:
9997:Aeroacoustics
9995:
9993:
9990:
9989:
9987:
9985:
9981:
9975:
9972:
9971:
9968:
9965:
9963:
9960:
9958:
9957:Charles's law
9955:
9953:
9950:
9948:
9945:
9944:
9941:
9938:
9937:
9934:
9931:
9929:
9926:
9924:
9921:
9919:
9916:
9914:
9911:
9909:
9906:
9902:
9901:Non-Newtonian
9899:
9897:
9894:
9893:
9892:
9889:
9887:
9884:
9882:
9879:
9877:
9874:
9872:
9869:
9867:
9864:
9862:
9861:Fluid statics
9859:
9858:
9855:
9852:
9851:
9849:
9847:
9843:
9835:
9832:
9830:
9827:
9825:
9822:
9821:
9820:
9817:
9816:
9813:
9810:
9809:
9804:
9801:
9800:
9799:
9796:
9792:
9789:
9787:
9784:
9783:
9782:
9779:
9777:
9774:
9772:
9769:
9767:
9764:
9763:
9760:
9757:
9756:
9751:
9748:
9746:
9743:
9742:
9741:
9738:
9732:
9729:
9728:
9727:
9724:
9722:
9719:
9717:
9714:
9713:
9712:
9709:
9703:
9700:
9698:
9695:
9694:
9693:
9690:
9688:
9685:
9683:
9680:
9676:
9673:
9671:
9668:
9667:
9666:
9663:
9659:
9656:
9655:
9654:
9651:
9649:
9646:
9644:
9641:
9639:
9636:
9634:
9631:
9630:
9629:
9626:
9625:
9622:
9619:
9618:
9616:
9614:
9610:
9606:
9600:
9599:Compatibility
9597:
9595:
9592:
9588:
9585:
9584:
9583:
9580:
9578:
9575:
9571:
9568:
9566:
9565:Cauchy stress
9563:
9562:
9561:
9558:
9557:
9553:
9552:
9549:
9546:
9544:
9541:
9537:
9534:
9532:
9529:
9527:
9524:
9522:
9519:
9517:
9516:Navier-Stokes
9514:
9513:
9512:
9509:
9507:
9504:
9503:
9499:
9498:
9496:
9492:
9486:
9483:
9481:
9478:
9476:
9473:
9471:
9468:
9466:
9463:
9462:
9460:
9456:
9452:
9444:
9439:
9437:
9432:
9430:
9425:
9424:
9421:
9407:
9404:
9398:
9383:
9377:
9373:
9369:
9365:
9358:
9351:
9343:
9339:
9335:
9331:
9327:
9323:
9320:(2): 81â126.
9319:
9315:
9308:
9300:
9296:
9292:
9288:
9284:
9280:
9276:
9272:
9268:
9264:
9257:
9249:
9245:
9241:
9237:
9230:
9222:
9215:
9200:
9196:
9192:
9188:
9184:
9180:
9176:
9172:
9168:
9161:
9147:
9145:9783662038857
9141:
9137:
9136:
9128:
9113:
9109:
9102:
9094:
9090:
9085:
9080:
9076:
9072:
9067:
9062:
9058:
9054:
9051:(4): e09328.
9050:
9046:
9042:
9035:
9027:
9023:
9019:
9015:
9011:
9008:(in French).
9007:
9003:
8996:
8988:
8984:
8979:
8974:
8970:
8966:
8962:
8958:
8954:
8947:
8939:
8935:
8930:
8925:
8921:
8917:
8913:
8909:
8905:
8901:
8897:
8893:
8889:
8882:
8874:
8870:
8866:
8862:
8858:
8854:
8850:
8843:
8841:
8832:
8828:
8824:
8820:
8816:
8812:
8808:
8804:
8800:
8793:
8791:
8782:
8778:
8774:
8770:
8766:
8762:
8758:
8751:
8749:
8747:
8738:
8734:
8730:
8726:
8722:
8718:
8710:
8702:
8698:
8694:
8690:
8683:
8675:
8671:
8668:: 1057â1079.
8667:
8663:
8656:
8654:
8645:
8638:
8636:
8634:
8625:
8621:
8617:
8613:
8609:
8605:
8601:
8597:
8593:
8589:
8585:
8578:
8570:
8566:
8562:
8558:
8554:
8550:
8546:
8542:
8538:
8531:
8523:
8519:
8515:
8511:
8507:
8503:
8499:
8495:
8491:
8484:
8476:
8472:
8468:
8464:
8460:
8453:
8445:
8441:
8437:
8433:
8429:
8425:
8421:
8417:
8413:
8406:
8398:
8394:
8390:
8386:
8382:
8375:
8367:
8363:
8359:
8355:
8348:
8340:
8336:
8332:
8328:
8321:
8313:
8309:
8305:
8301:
8297:
8293:
8289:
8285:
8278:
8276:
8274:
8265:
8261:
8257:
8253:
8249:
8245:
8241:
8237:
8236:AIChE Journal
8233:
8226:
8218:
8214:
8210:
8206:
8202:
8198:
8197:AIChE Journal
8194:
8187:
8179:
8175:
8171:
8167:
8163:
8159:
8155:
8151:
8147:
8143:
8142:AIChE Journal
8139:
8135:
8128:
8120:
8116:
8112:
8108:
8104:
8100:
8096:
8089:
8081:
8077:
8073:
8069:
8065:
8061:
8057:
8050:
8042:
8038:
8034:
8030:
8026:
8022:
8018:
8015:(in French).
8014:
8013:AIChE Journal
8007:
7999:
7992:
7984:
7980:
7976:
7972:
7968:
7964:
7960:
7956:
7952:
7945:
7937:
7933:
7929:
7925:
7921:
7917:
7913:
7906:
7904:
7895:
7891:
7887:
7883:
7879:
7873:
7869:
7865:
7858:
7849:
7841:
7837:
7833:
7829:
7825:
7821:
7814:
7806:
7802:
7798:
7794:
7790:
7786:
7782:
7778:
7771:
7763:
7756:
7748:
7742:
7738:
7731:
7727:
7717:
7714:
7712:
7709:
7707:
7704:
7702:
7699:
7697:
7694:
7693:
7685:
7682:
7680:
7677:
7675:
7672:
7670:
7667:
7664:
7661:
7658:
7656:
7653:
7651:
7648:
7645:
7644:Tait equation
7641:
7640:Tait equation
7638:
7637:
7626:
7623:
7620:
7617:
7614:
7611:
7608:
7606:
7603:
7601:
7598:
7597:
7593:
7590:
7587:
7584:
7581:
7578:
7575:
7572:
7569:
7567:
7566:Composition B
7564:
7563:
7559:
7556:
7553:
7550:
7547:
7544:
7541:
7538:
7535:
7533:
7530:
7529:
7510:
7506:
7498:
7484:
7477:
7461:
7457:
7449:
7433:
7429:
7421:
7405:
7398:
7382:
7375:
7357:
7354:
7350:
7342:
7324:
7320:
7312:
7294:
7290:
7282:
7279:
7278:
7275:
7259:
7255:
7232:
7229:
7225:
7202:
7198:
7175:
7171:
7150:
7128:
7124:
7101:
7097:
7076:
7056:
7036:
7014:
7010:
6989:
6985:
6979:
6975:
6971:
6968:
6959:
6944:
6938:
6934:
6930:
6924:
6920:
6916:
6911:
6907:
6903:
6899:
6895:
6892:
6888:
6881:
6876:
6872:
6867:
6862:
6859:
6855:
6851:
6848:
6842:
6837:
6833:
6829:
6823:
6820:
6816:
6809:
6804:
6800:
6795:
6790:
6787:
6783:
6779:
6776:
6773:
6759:
6757:
6752:
6748:
6744:
6740:
6739:polylogarithm
6736:
6732:
6728:
6722:
6718:
6714:
6710:
6705:
6690:
6685:
6678:
6674:
6670:
6665:
6654:
6648:
6640:
6634:
6629:
6626:
6623:
6619:
6609:
6606:
6603:
6598:
6594:
6590:
6582:
6580:
6570:
6568:
6550:
6546:
6523:
6519:
6498:
6476:
6471:
6467:
6461:
6457:
6453:
6450:
6442:
6432:
6418:
6396:
6369:
6354:
6339:
6335:
6329:
6321:
6318:
6313:
6305:
6302:
6293:
6285:
6283:
6278:
6275:
6270:
6256:
6252:
6247:
6241:
6237:
6233:
6230:
6226:
6222:
6219:
6214:
6210:
6200:
6184:
6180:
6159:
6139:
6130:
6114:
6110:
6106:
6103:
6100:
6094:
6091:
6088:
6082:
6079:
6076:
6068:
6066:
6062:
6058:
6043:
6040:
6026:
6020:
6016:
6012:
6008:
6004:
6001:
5996:
5992:
5988:
5984:
5978:
5974:
5968:
5965:
5962:
5958:
5952:
5947:
5944:
5941:
5937:
5931:
5926:
5923:
5920:
5916:
5912:
5908:
5902:
5898:
5894:
5890:
5886:
5883:
5878:
5874:
5870:
5866:
5860:
5856:
5850:
5847:
5844:
5840:
5834:
5829:
5826:
5823:
5819:
5813:
5808:
5805:
5802:
5798:
5794:
5790:
5786:
5783:
5779:
5775:
5772:
5767:
5763:
5759:
5755:
5749:
5745:
5739:
5736:
5733:
5729:
5723:
5718:
5715:
5712:
5709:
5705:
5699:
5694:
5691:
5688:
5684:
5680:
5675:
5671:
5667:
5663:
5657:
5653:
5647:
5644:
5641:
5637:
5631:
5626:
5623:
5620:
5617:
5613:
5607:
5602:
5599:
5596:
5592:
5588:
5556:
5547:
5544:
5527:
5523:
5500:
5496:
5486:
5469:
5465:
5461:
5456:
5453:
5450:
5445:
5440:
5436:
5430:
5427:
5404:
5401:
5393:
5390:
5387:
5373:
5369:
5363:
5360:
5357:
5321:
5314:
5308:
5305:
5297:
5294:
5291:
5285:
5267:
5264:
5260:
5256:
5252:
5248:
5238:
5235:
5226:
5224:
5220:
5216:
5211:
5201:
5187:
5182:
5175:
5170:
5166:
5161:
5158:
5152:
5148:
5145:
5141:
5133:
5128:
5124:
5120:
5115:
5112:
5108:
5099:
5094:
5090:
5084:
5079:
5075:
5068:
5064:
5058:
5051:
5046:
5042:
5038:
5033:
5026:
5021:
5017:
5013:
5008:
5001:
4997:
4993:
4988:
4985:
4981:
4975:
4971:
4968:
4962:
4959:
4951:
4948:
4944:
4929:
4925:
4920:
4914:
4911:
4906:
4903:
4899:
4895:
4892:
4887:
4883:
4878:
4870:
4866:
4862:
4857:
4852:
4849:
4844:
4841:
4838:
4835:
4832:
4829:
4825:
4821:
4816:
4812:
4807:
4799:
4795:
4789:
4785:
4779:
4772:
4768:
4762:
4758:
4752:
4745:
4741:
4735:
4731:
4725:
4720:
4716:
4712:
4709:
4706:
4701:
4697:
4692:
4688:
4685:
4682:
4679:
4676:
4673:
4664:
4662:
4642:
4635:
4620:
4613:
4612:
4611:
4608:
4594:
4588:
4584:
4580:
4577:
4573:
4569:
4566:
4562:
4556:
4552:
4548:
4545:
4542:
4538:
4530:
4526:
4519:
4515:
4511:
4505:
4500:
4496:
4491:
4485:
4482:
4477:
4474:
4470:
4466:
4463:
4458:
4454:
4449:
4443:
4440:
4435:
4432:
4429:
4426:
4423:
4420:
4416:
4412:
4407:
4403:
4398:
4390:
4386:
4380:
4376:
4370:
4363:
4359:
4353:
4349:
4343:
4336:
4332:
4326:
4322:
4316:
4311:
4307:
4303:
4300:
4297:
4292:
4288:
4283:
4279:
4276:
4273:
4270:
4267:
4264:
4255:
4245:
4243:
4239:
4235:
4231:
4227:
4223:
4219:
4215:
4211:
4206:
4193:
4190:
4183:
4178:
4174:
4170:
4165:
4158:
4153:
4149:
4145:
4140:
4133:
4129:
4125:
4120:
4117:
4114:
4108:
4105:
4098:
4094:
4090:
4078:
4063:
4047:
4043:
4034:
4030:
4025:
4015:
4013:
4009:
4005:
3989:
3985:
3981:
3972:
3958:
3954:
3951:
3943:
3939:
3935:
3927:
3918:
3914:
3908:
3901:
3897:
3893:
3881:
3878:
3875:
3872:
3866:
3860:
3856:
3852:
3848:
3842:
3839:
3835:
3831:
3822:
3818:
3815:
3812:
3809:
3801:
3787:
3784:
3776:
3767:
3759:
3755:
3751:
3730:
3727:
3719:
3710:
3702:
3698:
3694:
3684:
3671:
3665:
3662:
3654:
3645:
3637:
3633:
3630:
3627:
3623:
3617:
3606:
3602:
3598:
3594:
3580:
3576:
3567:
3563:
3557:
3553:
3547:
3538:
3534:
3530:
3522:
3513:
3509:
3500:
3497:
3494:
3491:
3482:
3477:
3474:
3464:
3445:
3441:
3437:
3434:
3431:
3425:
3417:
3395:
3371:
3368:
3360:
3351:
3343:
3339:
3336:
3333:
3329:
3323:
3312:
3308:
3304:
3300:
3286:
3282:
3273:
3269:
3263:
3259:
3255:
3246:
3242:
3236:
3227:
3221:
3217:
3213:
3205:
3202:
3199:
3196:
3187:
3184:
3176:
3162:
3155:and pressure
3142:
3122:
3102:
3094:
3090:
3074:
3054:
3040:
3024:
3020:
2997:
2993:
2972:
2967:
2963:
2959:
2956:
2948:
2930:
2926:
2921:
2915:
2911:
2907:
2904:
2896:
2880:
2860:
2854:
2851:
2848:
2842:
2839:
2836:
2828:
2823:
2810:
2807:
2804:
2801:
2798:
2795:
2792:
2789:
2786:
2780:
2777:
2774:
2771:
2768:
2762:
2753:
2740:
2737:
2734:
2731:
2728:
2725:
2722:
2714:
2713:ideal gas law
2702:Ideal gas law
2699:
2685:
2665:
2642:
2639:
2636:
2630:
2627:
2622:
2618:
2610:
2602:
2597:
2593:
2589:
2584:
2581:
2578:
2574:
2566:
2565:
2564:
2561:
2559:
2555:
2551:
2547:
2543:
2527:
2523:
2512:
2502:
2499:
2494:
2490:
2485:
2481:
2478:
2473:
2469:
2465:
2437:
2434:
2424:
2416:
2408:
2404:
2400:
2393:
2389:
2382:
2381:
2380:ideal gas law
2376:
2360:
2355:
2351:
2345:
2340:
2337:
2334:
2330:
2326:
2321:
2317:
2313:
2310:
2307:
2302:
2298:
2294:
2289:
2285:
2281:
2272:
2251:
2242:
2240:
2225:
2218:
2214:
2208:
2204:
2198:
2191:
2187:
2181:
2177:
2166:
2162:
2161:Charles's law
2158:
2153:
2151:
2150:Edme Mariotte
2135:
2106:
2103:
2100:
2091:
2087:
2083:
2057:
2053:
2045:
2028:
2024:
2016:
1999:
1995:
1987:
1980:
1964:
1957:
1954:
1936:
1933:
1909:
1905:
1897:
1894:
1878:
1871:
1870:
1869:
1867:
1863:
1859:
1854:
1852:
1847:
1845:
1842:
1841:perfect fluid
1838:
1834:
1833:neutron stars
1828:
1826:
1810:
1790:
1770:
1761:
1748:
1745:
1739:
1736:
1733:
1730:
1727:
1721:
1712:
1710:
1709:ideal gas law
1692:
1687:
1685:
1680:
1678:
1673:
1672:
1670:
1669:
1664:
1656:
1655:
1654:
1653:
1646:
1643:
1641:
1638:
1636:
1635:Self-assembly
1633:
1631:
1628:
1627:
1621:
1620:
1612:
1609:
1607:
1606:van der Waals
1604:
1602:
1599:
1597:
1594:
1592:
1589:
1587:
1584:
1582:
1579:
1577:
1574:
1572:
1569:
1567:
1564:
1562:
1559:
1557:
1554:
1552:
1549:
1547:
1544:
1542:
1539:
1537:
1534:
1532:
1531:von Helmholtz
1529:
1527:
1524:
1522:
1519:
1517:
1514:
1512:
1509:
1507:
1504:
1502:
1499:
1497:
1494:
1492:
1489:
1487:
1484:
1482:
1479:
1478:
1471:
1470:
1459:
1456:
1454:
1451:
1450:
1449:
1448:
1441:
1438:
1437:
1435:
1434:
1428:
1425:
1423:
1420:
1419:
1417:
1416:
1412:
1411:
1405:
1404:
1397:
1394:
1393:
1386:
1383:
1382:
1375:
1374:
1373:
1372:
1369:
1366:
1365:
1360:
1357:
1355:
1352:
1350:
1346:
1342:
1341:
1337:
1334:
1333:
1331:
1330:
1326:
1325:
1319:
1316:
1314:
1311:
1309:
1306:
1304:
1301:
1299:
1296:
1294:
1291:
1289:
1286:
1285:
1283:
1282:
1279:
1276:
1275:
1270:
1267:
1266:
1262:
1259:
1257:
1254:
1252:
1249:
1248:
1246:
1245:
1241:
1240:
1231:
1228:
1227:
1223:
1222:
1202:
1199:
1196:
1193:
1190:
1184:
1181:
1178:
1172:
1164:
1161:
1147:
1144:
1141:
1138:
1135:
1129:
1126:
1123:
1117:
1109:
1106:
1092:
1089:
1086:
1083:
1080:
1074:
1071:
1068:
1062:
1054:
1051:
1034:
1031:
1028:
1022:
1014:
1011:
1010:
1005:
1002:
1000:
997:
996:
992:
987:
986:
979:
978:
974:
972:
969:
967:
964:
962:
959:
958:
954:
953:Ideal gas law
951:
949:
946:
944:
941:
939:
936:
935:
931:
926:
925:
899:
889:
875:
868:
867:
852:
842:
828:
821:
820:
817:
803:
800:
793:
790:
787:
786:
767:
757:
743:
736:
735:
720:
710:
696:
689:
688:
685:
671:
668:
665:
658:
655:
652:
651:
632:
622:
608:
601:
600:
585:
575:
561:
554:
553:
550:
536:
533:
526:
523:
520:
519:
513:
510:
509:
506:
501:
500:
489:
486:
484:
483:Vapor quality
481:
479:
478:
473:
470:
468:
467:
462:
459:
456:
452:
451:
446:
443:
442:
441:
440:
437:
434:
433:
427:
424:
422:
419:
418:
416:
415:
412:
409:
408:
403:
400:
398:
395:
394:
393:
392:
388:
384:
377:
372:
371:
360:
357:
355:
352:
350:
347:
346:
345:
344:
341:
338:
337:
332:
329:
327:
324:
322:
321:Reversibility
319:
317:
314:
312:
309:
307:
304:
302:
299:
297:
294:
292:
289:
287:
284:
282:
279:
277:
274:
273:
272:
271:
268:
265:
264:
259:
256:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
226:
224:
221:
220:
219:
218:
215:
212:
211:
206:
203:
201:
198:
196:
195:Closed system
193:
192:
189:
184:
183:
175:
172:
170:
167:
165:
162:
160:
157:
156:
152:
147:
146:
139:
135:
132:
131:
127:
124:
122:
119:
117:
114:
112:
109:
108:
101:
100:
96:
90:
86:
85:
82:
79:
78:
75:
73:
69:
65:
61:
57:
53:
49:
45:
41:
37:
33:
26:
22:
10971:Applications
10922:size scaling
10752:
10650:Superheating
10609:
10523:Vaporization
10518:Triple point
10513:Supercooling
10478:Lambda point
10428:Condensation
10345:Time crystal
10323:Other states
10263:Quantum Hall
10020:Smart fluids
9913:Pascal's law
9745:Frictionless
9664:
9594:Large strain
9582:Small strain
9397:
9385:. Retrieved
9363:
9350:
9317:
9313:
9307:
9269:(1): 29â90.
9266:
9262:
9256:
9239:
9235:
9229:
9220:
9214:
9202:. Retrieved
9174:
9170:
9160:
9149:, retrieved
9134:
9127:
9115:. Retrieved
9111:
9101:
9048:
9044:
9034:
9009:
9005:
8995:
8963:(1): 51â58.
8960:
8956:
8946:
8895:
8891:
8881:
8856:
8852:
8806:
8802:
8764:
8760:
8720:
8716:
8709:
8692:
8688:
8682:
8665:
8661:
8643:
8591:
8587:
8577:
8544:
8540:
8530:
8497:
8493:
8483:
8466:
8462:
8452:
8419:
8415:
8405:
8388:
8384:
8374:
8357:
8353:
8347:
8330:
8326:
8320:
8287:
8283:
8239:
8235:
8225:
8200:
8196:
8186:
8145:
8141:
8127:
8102:
8098:
8088:
8063:
8059:
8049:
8016:
8012:
8006:
7997:
7991:
7958:
7954:
7944:
7919:
7915:
7863:
7857:
7848:
7823:
7819:
7813:
7780:
7776:
7770:
7761:
7755:
7736:
7730:
7643:
6960:
6765:
6750:
6746:
6737:, Li is the
6730:
6726:
6720:
6716:
6712:
6708:
6706:
6583:
6576:
6438:
6355:
6294:
6291:
6279:
6273:
6271:
6201:
6131:
6069:
6054:
6041:
5548:
5545:
5487:
5273:
5244:
5232:
5207:
4952:
4949:
4945:
4665:
4658:
4609:
4257:
4241:
4237:
4233:
4229:
4225:
4221:
4218:coefficients
4207:
4080:
4027:
4011:
3973:
3802:
3685:
3177:
3175:is given by
3046:
2824:
2754:
2710:
2657:
2562:
2407:gas constant
2402:
2395:
2391:
2384:
2378:
2243:
2239:Dalton's law
2154:
2086:Robert Boyle
2080:
1953:molar volume
1891:, number of
1855:
1848:
1829:
1762:
1713:
1705:
1496:Carathéodory
1427:Heat engines
1399:
1388:
1377:
1359:Motive power
1344:
1004:Free entropy
975:
475:
474: /
464:
463: /
455:introduction
448:
447: /
386:
349:Heat engines
222:
136: /
39:
29:
10962:von Neumann
10832:force field
10824:percolation
10559:Latent heat
10508:Sublimation
10453:Evaporation
10388:Ferromagnet
10383:Ferrimagnet
10365:Dark matter
10297:High energy
10035:Ferrofluids
9952:Boyle's law
9638:Hooke's law
9577:Deformation
9554:Definitions
9242:: 290â293.
8898:(12): 169.
8767:(1): 1â39.
8469:: 105â113.
8360:: 150â157.
6741:, ζ is the
4633:is pressure
3800:reduces to
2264:species as:
2082:Boyle's law
1981:â 8.3144621
1318:Synergetics
999:Free energy
445:Temperature
306:Quasistatic
301:Isenthalpic
258:Instruments
248:Equilibrium
200:Open system
134:Equilibrium
116:Statistical
60:temperature
11032:Categories
10819:Heisenberg
10574:Volatility
10537:Quantities
10498:Regelation
10473:Ionization
10448:Deposition
10400:Superglass
10370:Antimatter
10304:QCD matter
10283:Supersolid
10278:Superfluid
10241:Low energy
10090:Gay-Lussac
10057:Scientists
9947:Atmosphere
9812:Structures
9786:J-integral
9750:Frictional
9711:Plasticity
9648:Orthotropy
9628:Elasticity
9531:Archimedes
9526:Poiseuille
9480:Vibrations
9449:Topics in
9112:Ucrl-52997
7922:: 112772.
7877:087201293X
7722:References
6961:The ratio
1630:Nucleation
1474:Scientists
1278:Philosophy
991:Potentials
354:Heat pumps
311:Polytropic
296:Isentropic
286:Isothermal
10942:Boltzmann
10865:H-theorem
10743:Ensembles
10065:Bernoulli
10047:Rheometer
10042:Rheometry
9984:Acoustics
9896:Newtonian
9891:Viscosity
9521:Bernoulli
9475:Acoustics
9458:Divisions
9387:31 August
9342:0895-7959
9299:250909120
9291:0034-4885
9204:31 August
9199:129899060
9151:31 August
9117:31 August
9075:2405-8440
9026:1290-0729
8987:1674-9871
8920:0195-928X
8873:0047-2689
8831:0047-2689
8781:116961558
8624:121383911
8616:0022-4715
8569:0021-9606
8522:0021-9606
8444:0031-899X
8304:0378-3812
8290:: 31â38.
8264:0001-1541
8170:0001-1541
8119:0888-5885
8080:0888-5885
8041:1547-5905
7983:0026-8976
7936:224844789
7797:0009-2665
7485:ω
7291:ρ
7172:ρ
7151:ω
7037:ρ
7011:ρ
6990:ρ
6976:ρ
6931:ω
6904:−
6896:
6868:ω
6863:−
6830:−
6824:
6796:ω
6791:−
6691:α
6655:α
6649:ζ
6635:
6624:α
6520:ρ
6458:ρ
6419:ν
6393:Γ
6366:Γ
6336:ν
6326:Γ
6319:ν
6310:Γ
6257:ρ
6223:γ
6160:γ
6107:γ
6104:−
6092:−
6089:γ
6083:ρ
6017:δ
6013:−
6005:
5985:τ
5975:δ
5938:∑
5917:∑
5899:δ
5895:−
5887:
5867:τ
5857:δ
5820:∑
5799:∑
5787:δ
5784:−
5776:
5756:τ
5746:δ
5716:−
5706:∑
5685:∑
5664:τ
5654:δ
5624:−
5614:∑
5593:∑
5497:ρ
5466:ρ
5462:ρ
5454:δ
5428:τ
5394:δ
5388:τ
5364:δ
5358:τ
5298:ρ
5223:Mie fluid
5162:γ
5159:−
5149:
5121:γ
5113:β
4926:ρ
4896:α
4884:ρ
4845:−
4839:−
4813:ρ
4780:−
4726:−
4713:−
4680:ρ
4643:ρ
4585:ρ
4581:γ
4578:−
4570:
4553:ρ
4549:γ
4516:ρ
4497:ρ
4467:α
4455:ρ
4436:−
4430:−
4404:ρ
4371:−
4317:−
4304:−
4271:ρ
4194:⋯
4004:Fermi gas
3955:⋯
3898:ℏ
3849:π
3843:±
3785:≪
3756:μ
3728:≪
3699:μ
3663:±
3634:μ
3631:−
3586:∞
3577:∫
3564:ℏ
3554:π
3426:μ
3369:±
3340:μ
3337:−
3292:∞
3283:∫
3270:ℏ
3260:π
3067:and spin
2905:γ
2881:ρ
2852:−
2849:γ
2843:ρ
2796:−
2628:−
2540:In 1873,
2513:∘
2458:, giving:
2425:∘
2373:In 1834,
2331:∑
2311:⋯
1611:Waterston
1561:von Mayer
1516:de Donder
1506:Clapeyron
1486:Boltzmann
1481:Bernoulli
1442:Education
1413:Timelines
1197:−
1142:−
930:Equations
897:∂
850:∂
801:α
765:∂
718:∂
672:−
666:β
630:∂
583:∂
291:Adiabatic
281:Isochoric
267:Processes
228:Ideal gas
111:Classical
46:relating
36:chemistry
10952:Tsallis
10635:Spinodal
10583:Concepts
10463:Freezing
10007:Rheology
9918:Pressure
9886:Buoyancy
9670:Hugoniot
9093:35520603
8938:34121788
8312:53310898
8178:96417239
7886:70184683
7805:18125401
7711:Real gas
7696:Gas laws
7690:See also
7600:PBX 9501
7280:Material
6729:) where
6579:Bose gas
5379:residual
4008:Bose gas
2556:and the
1702:Overview
1663:Category
1601:Thompson
1511:Clausius
1491:Bridgman
1345:Vis viva
1327:Theories
1261:Gas laws
1053:Enthalpy
461:Pressure
276:Isobaric
233:Real gas
121:Chemical
104:Branches
52:pressure
10947:Shannon
10934:Entropy
10595:Binodal
10483:Melting
10418:Boiling
10335:Crystal
10330:Colloid
10080:Charles
9923:Liquids
9819:Bending
9776:Fatigue
9322:Bibcode
9271:Bibcode
9179:Bibcode
9084:9062208
9053:Bibcode
9045:Heliyon
8965:Bibcode
8929:8191392
8900:Bibcode
8811:Bibcode
8725:Bibcode
8596:Bibcode
8549:Bibcode
8502:Bibcode
8424:Bibcode
8244:Bibcode
8205:Bibcode
8150:Bibcode
8021:Bibcode
7963:Bibcode
7828:Bibcode
6733:is the
6715:is exp(
6565:is the
6274:already
5221:or the
3414:is the
2893:is the
2825:If the
2405:is the
2090:Mercury
1985:J/mol·K
1586:Smeaton
1581:Rankine
1571:Onsager
1556:Maxwell
1551:Massieu
1256:Entropy
1251:General
1242:History
1232:Culture
1229:History
453: (
450:Entropy
387:italics
188:Systems
32:physics
10796:Models
10704:Theory
10223:Plasma
10204:Liquid
10125:Awards
10115:Stokes
10110:Navier
10105:Newton
10100:Pascal
10075:Cauchy
9974:Plasma
9854:Fluids
9633:linear
9621:Solids
9560:Stress
9536:Pascal
9378:
9340:
9297:
9289:
9197:
9142:
9091:
9081:
9073:
9024:
8985:
8936:
8926:
8918:
8871:
8829:
8779:
8622:
8614:
8567:
8520:
8442:
8310:
8302:
8262:
8176:
8168:
8117:
8078:
8039:
7981:
7934:
7894:947455
7892:
7884:
7874:
7803:
7795:
7743:
7634:Others
7526:(GPa)
7310:(g/cm)
6745:, and
6707:where
6613:
6491:where
6357:Where
6132:where
6063:, and
4610:where
3387:where
2873:where
2658:where
2506:
2503:273.15
2441:
2438:273.15
2421:
1983:
1866:Kelvin
1763:where
1576:Planck
1566:Nernst
1541:Kelvin
1501:Carnot
791:
656:
524:
466:Volume
381:Note:
340:Cycles
169:Second
159:Zeroth
56:volume
11005:chaos
10957:RĂ©nyi
10814:Potts
10809:Ising
10213:Vapor
10199:Solid
10192:State
10095:Hooke
10085:Euler
10070:Boyle
9940:Gases
9697:Creep
9609:Solid
9360:(PDF)
9295:S2CID
9195:S2CID
8777:S2CID
8620:S2CID
8308:S2CID
8174:S2CID
7932:S2CID
7627:10.2
7615:18.02
7612:852.4
7604:1.844
7594:8.50
7582:7.678
7579:524.2
7570:1.717
7560:6.00
7548:3.747
7545:373.8
7536:1.630
7419:(GPa)
7396:(GPa)
7373:(GPa)
7340:(m/s)
5420:with
2277:total
1893:moles
1624:Other
1591:Stahl
1546:Lewis
1536:Joule
1526:Gibbs
1521:Duhem
214:State
174:Third
164:First
72:stars
68:solid
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42:is a
38:, an
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9611:and
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9119:2018
9089:PMID
9071:ISSN
9022:ISSN
8983:ISSN
8934:PMID
8916:ISSN
8869:ISSN
8827:ISSN
8612:ISSN
8565:ISSN
8518:ISSN
8440:ISSN
8300:ISSN
8260:ISSN
8166:ISSN
8115:ISSN
8076:ISSN
8037:ISSN
7979:ISSN
7890:OCLC
7882:LCCN
7872:ISBN
7801:PMID
7793:ISSN
7741:ISBN
7624:0.38
7618:4.55
7609:36.3
7591:0.35
7588:1.10
7585:4.20
7576:29.5
7573:7980
7557:0.35
7554:0.90
7551:4.15
7542:21.0
7539:6930
7143:and
5266:al.
3461:the
3418:and
1596:Tait
426:Heat
421:Work
151:Laws
34:and
10209:Gas
9675:JWL
9368:doi
9330:doi
9279:doi
9244:doi
9187:doi
9079:PMC
9061:doi
9014:doi
8973:doi
8924:PMC
8908:doi
8861:doi
8819:doi
8769:doi
8733:doi
8721:106
8697:doi
8670:doi
8604:doi
8557:doi
8510:doi
8471:doi
8467:103
8432:doi
8420:182
8393:doi
8389:264
8362:doi
8358:382
8335:doi
8292:doi
8252:doi
8213:doi
8158:doi
8107:doi
8068:doi
8029:doi
7971:doi
7924:doi
7920:523
7836:doi
7785:doi
7621:1.3
7532:TNT
6893:exp
6821:exp
6581:is
6439:An
6002:exp
5884:exp
5773:exp
5146:exp
4567:exp
4035:of
2949:),
1439:Art
385:in
74:.
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11034::
10760::
10211:/
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9318:16
9316:.
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9110:.
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